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on Microeconomics |
| By: | Maria Arbatskaya (Emory University); Hideo Konishi (Boston College) |
| Abstract: | This paper studies strategic effort disclosure in dynamic team contests. Two teams of two players compete in a Tullock contest with teammates' sequential efforts aggregated across two periods using a Cobb-Douglas production function. We examine how equilibrium efforts and winning probabilities are affected by the teams' communication policies: no communication, private communication (efforts shared internally with stage-2 teammates), and public communication (efforts disclosed to stage-2 rivals as well. To describe asymmetric information generated by privately observable efforts for each communication policy profile, we use perfect Bayesian equilibrium with an appropriate belief refinement for multi-stage complete information games. In the unique positive-effort equilibrium, the optimal choice of a communication strategy dff§ers for the favorite (the strong team) and the underdog (the weak team). Private communication only benefits the underdog team, fostering effort complementarity and improving their chances of winning and payoffs. In contrast, the favorite team prefers either public or no communication to deter rival efforts or avoid intra-team free-riding. Importantly, endogenous communication policies reshape competitive dynamics, with private disclosure of efforts serving as a strategic equalizer for weaker teams. |
| Keywords: | team contest, complementarity in efforts, communication policy, commitment, information |
| JEL: | C72 D23 D74 |
| Date: | 2025–07–21 |
| URL: | https://d.repec.org/n?u=RePEc:boc:bocoec:1094 |
| By: | Ivan Geffner; Caspar Oesterheld; Vincent Conitzer |
| Abstract: | We examine normal-form games in which players may \emph{pre-commit} to outcome-contingent transfers before choosing their actions. In the one-shot version of this model, Jackson and Wilkie showed that side contracting can backfire: even a game with a Pareto-optimal Nash equilibrium can devolve into inefficient equilibria once unbounded, simultaneous commitments are allowed. The root cause is a prisoner's dilemma effect, where each player can exploit her commitment power to reshape the equilibrium in her favor, harming overall welfare. To circumvent this problem we introduce a \emph{staged-commitment} protocol. Players may pledge transfers only in small, capped increments over multiple rounds, and the phase continues only with unanimous consent. We prove that, starting from any finite game $\Gamma$ with a non-degenerate Nash equilibrium $\vec{\sigma}$, this protocol implements every welfare-maximizing payoff profile that \emph{strictly} Pareto-improves $\vec{\sigma}$. Thus, gradual and bounded commitments restore the full efficiency potential of side payments while avoiding the inefficiencies identified by Jackson and Wilkie. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.07147 |
| By: | Förster, Manuel (Center for Mathematical Economics, Bielefeld University); Närmann, Fynn Louis (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We study a dynamic game in which a monopolistic seller sequentially discloses information about a binary state to a consumer through priced experiments. The consumer privately observes a binary signal which influences her willingness to pay for information. We show that if buyer types favor different actions but their willingness to pay for a state-revealing test is sufficiently close, then the seller can commit to a sequence of priced experiments that extracts the entire surplus of both consumer types simultaneously. The optimal sequence of experiments is such that the high-valuation type assigns a higher probability to outcomes that trigger further information acquisition, thus creating a difference in expected costs. As a key element of the construction, we introduce an ‘encryption protocol’ under which the consumer faces a stopping problem. We then characterize situations in which the seller strictly benefits from a dynamic selling strategy when perfect price discrimination is not feasible. Finally, we illustrate our framework in the context of medical diagnostic testing, showing that a free test followed by a state-revealing test is often sufficient to improve revenue in comparison with a static approach. |
| Keywords: | Information design, dynamic mechanism, selling information, encryption, price discrimination |
| Date: | 2025–07–03 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:749 |
| By: | Patrick Lederer |
| Abstract: | Social decision schemes (SDSs) map the voters' preferences over multiple alternatives to a probability distribution over these alternatives. In a seminal result, Gibbard (1977) has characterized the set of SDSs that are strategyproof with respect to all utility functions and his result implies that all such SDSs are either unfair to the voters or alternatives, or they require a significant amount of randomization. To circumvent this negative result, we propose the notion of $U$-strategyproofness which postulates that only voters with a utility function in a predefined set $U$ cannot manipulate. We then analyze the tradeoff between $U$-strategyproofness and various decisiveness notions that restrict the amount of randomization of SDSs. In particular, we show that if the utility functions in the set $U$ value the best alternative much more than other alternatives, there are $U$-strategyproof SDSs that choose an alternative with probability $1$ whenever all but $k$ voters rank it first. On the negative side, we demonstrate that $U$-strategyproofness is incompatible with Condorcet-consistency if the set $U$ satisfies minimal symmetry conditions. Finally, we show that no ex post efficient and $U$-strategyproof SDS can be significantly more decisive than the uniform random dictatorship if the voters are close to indifferent between their two favorite alternatives. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.16195 |
| By: | Saeed Alaei; Shuchi Chawla; Zhiyi Huang; Ali Makhdoumi; Azarakhsh Malekian |
| Abstract: | We consider a mechanism design setting with a single item and a single buyer who is uncertain about the value of the item. Both the buyer and the seller have a common model for the buyer's value, but the buyer discovers her true value only upon receiving the item. Mechanisms in this setting can be interpreted as randomized refund mechanisms, which allocate the item at some price and then offer a (partial and/or randomized) refund to the buyer in exchange for the item if the buyer is unsatisfied with her purchase. Motivated by their practical importance, we study the design of optimal deterministic mechanisms in this setting. We characterize optimal mechanisms as virtual value maximizers for both continuous and discrete type settings. We then use this characterization, along with bounds on the menu size complexity, to develop efficient algorithms for finding optimal and near-optimal deterministic mechanisms. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.04148 |
| By: | Hans Gersbach; Arthur Schichl; Oriol Tejada |
| Abstract: | Which level of voting costs is optimal in a democracy? This paper argues that intermediate voting costs - what we term a "Midcost democracy" - should be avoided, as they fail to ensure that electoral outcomes reflect the preferences of the majority. We study a standard binary majority decision in which a majority of the electorate prefers alternative A over alternative B. The population consists of partisan voters, who always participate, and non-partisan voters, who vote only when they believe their participation could be pivotal, given that voting entails a cost. We show that the probability of the majority-preferred alternative A winning is non-monotonic in the level of voting costs. Specifically, when voting costs are either high or negligible, alternative A wins in all equilibria. However, at intermediate cost levels, this alignment breaks down. These findings suggest that democratic systems should avoid institutional arrangements that lead to moderate voting costs, as they may undermine the majority principle. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.07300 |
| By: | Shashwat Khare; Souvik Roy |
| Abstract: | We study many-to-one matching problems between institutions and individuals, where each institution may be matched to multiple individuals. The matching market includes couples, who view pairs of institutions as complementary. Institutions' preferences over sets of individuals are assumed to satisfy responsiveness, whereas couples' preferences over pairs of institutions may violate responsiveness. In this setting, we first assume that all institutions share a common preference ordering over individuals, and we establish: (i) a complete characterization of all couples' preference profiles for which a stable matching exists, under the additional assumption that couples violate responsiveness only to ensure co-location at the same institution, and (ii) a necessary and sufficient condition on the common institutional preference such that a stable matching exists when couples may violate responsiveness arbitrarily. Next, we relax the common preference assumption, requiring institutions to share a common ranking only over the members of each couple. Under this weaker assumption, we provide: (i) a complete characterization of all couples' preferences for which a stable matching exists, and (ii) a sufficient condition on individuals' preferences that guarantees the existence of a stable matching. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.07490 |
| By: | Zizhe Xia |
| Abstract: | I study whether and which expert incentives can be provided at what cost when the states of the world become non-contractible, but there is some noisy observation about the states that can be contracted upon. A principal hires an agent to acquire costly information about the states, but it is not possible to pay the agent based on the realized states. Instead, the principal has access to a noisy (Blackwell) experiment about the states, and can pay bonuses based on its realization. The agent is risk neutral and protected by limited liability. I completely characterize what the principal can incentivize the agent to learn, and how to design contracts to minimize the costs to provide such incentives. I then study which contractible information is always better at incentive provision. This gives rise to a novel order on information. In the binary-binary case, this order is characterized by larger differences in the likelihood ratios of the two realizations. My results provide insights into what information is better for evaluating expert predictions. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.10170 |
| By: | Hu Fu; Tao Lin |
| Abstract: | In non-truthful auctions such as first-price and all-pay auctions, the independent strategic behaviors of bidders, with the corresponding equilibrium notion -- Bayes Nash equilibria -- are notoriously difficult to characterize and can cause undesirable outcomes. An alternative approach to designing better auction systems is to coordinate the bidders: let a mediator make incentive-compatible recommendations of correlated bidding strategies to the bidders, namely, implementing a Bayes correlated equilibrium (BCE). The implementation of BCE, however, requires knowledge of the distribution of bidders' private valuations, which is often unavailable. We initiate the study of the sample complexity of learning Bayes correlated equilibria in non-truthful auctions. We prove that the BCEs in a large class of non-truthful auctions, including first-price and all-pay auctions, can be learned with a polynomial number $\tilde O(\frac{n}{\varepsilon^2})$ of samples from the bidders' value distributions. Our technique is a reduction to the problem of estimating bidders' expected utility from samples, combined with an analysis of the pseudo-dimension of the class of all monotone bidding strategies of bidders. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.02801 |
| By: | Souvik Roy; Agamani Saha |
| Abstract: | This paper explores a novel extension of dynamic matching theory by analyzing a three-way matching problem involving agents from three distinct populations, each with two possible types. Unlike traditional static or two-way dynamic models, our setting captures more complex team-formation environments where one agent from each of the three populations must be matched to form a valid team. We consider two preference structures: assortative or homophilic, where agents prefer to be matched with others of the same type, and dis-assortative or heterophilic, where diversity within the team is valued. Agents arrive sequentially and face a trade-off between matching immediately or waiting for a higher quality match in the future albeit with a waiting cost. We construct and analyze the corresponding transition probability matrices for each preference regime and demonstrate the existence and uniqueness of stationary distributions. Our results show that stable and efficient outcomes can arise in dynamic, multi-agent matching environments, offering a deeper understanding of how complex matching processes evolve over time and how they can be effectively managed. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.06126 |
| By: | Mononen, Lasse (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We characterize the empirical content of expected utility. We show that the empirical content of the expected utility theory is contained in completeness, transitivity, and strong independence axioms. However, under commonly used weaker forms of independence axiom, the continuity adds empirical content in the expected utility theory. This formalizes and makes exact the ubiquitous claim that the continuity axiom is a technical axiom without empirical content in the expected utility theory. |
| Date: | 2025–08–15 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:737 |
| By: | Xinli Guo |
| Abstract: | We study soft budget constraints in multi-tier public finance when an upper-tier government uses two instruments: an ex-ante grant schedule and an ex-post rescue. Under convex rescue costs and standard primitives, the three-stage leader-follower problem collapses to one dimensional screening with a single allocation index: the cap on realized rescue. A hazard-based characterization delivers a unified rule that nests (i) no rescue, (ii) a threshold-cap with commitment, and (iii) a threshold--linear--cap without commitment. The knife-edge for eliminating bailouts compares the marginal cost at the origin to the supremum of a virtual weight, and the comparative statics show how greater curvature tightens caps while discretion shifts transfers toward front loading by lowering the effective grant weight. The framework provides a portable benchmark for mechanism design and yields testable implications for policy and empirical work on intergovernmental finance. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.10724 |
| By: | Ferrari, Giorgio (Center for Mathematical Economics, Bielefeld University); Pajola, Anna (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We study a mean-field game of optimal stopping and investigate the existence of strong solutions via a connection with the Bank-El Karoui’s representation problem. Under certain continuity assumptions, where the common noise is generated by a countable partition, we show that a strong randomized mean-field equilibrium exists, in which the mean-field interaction term is adapted to the common noise and the stopping time is randomized. Furthermore, under suitable monotonicity assumptions and for a general common noise, we provide a comparative statics analysis of the set of strong mean-field equilibria with strict equilibrium stopping times. |
| Keywords: | mean-field game of optimal stopping, randomized stopping time, common noise, Bank-El Karoui’s representation theorem |
| Date: | 2025–07–25 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:751 |
| By: | Foros, Øystein (Dept. of Business and Management Science, Norwegian School of Economics and Business Administration); Kind, Hans Jarle (Dept. of Economics, Norwegian School of Economics and Business Administration); Shaffer, Greg (Simon Business School, University of Rochester) |
| Abstract: | This paper uses a Nash-in-Nash bargaining framework to consider why suppliers and retailers sometimes prefer to negotiate over linear contracts rather than over more sophisticated contracts such as two-part tariffs, and why, when they do negotiate over more sophisticated contracts, we often see negative fixed fees (slotting fees). We compare profits under the two forms of contracts and find under weak conditions that when negative fixed fees would arise in the case of two-part tari↵s, at least one side and often both sides will prefer this outcome to the outcome that would arise with linear contracts. In contrast, the opposite holds when positive fixed fees would arise in the case of two-part tariffs. Using linear demands, we demonstrate that retailers always favor negotiating over two-part tariffs when the fixed fees are negative, and prefer linear contracts when the fixed fees are positive. Suppliers generally share these preferences, unless they possess particularly strong bargaining power relative to retailers. Our findings have implications for retailer buyer power and are broadly consistent with stylized facts from the U.S. grocery industry. |
| Keywords: | Nash-in-Nash bargaining; Two-part tariffs; Linear contracts; Slotting fees; Retailer buyer power |
| JEL: | D04 L50 |
| Date: | 2025–08–17 |
| URL: | https://d.repec.org/n?u=RePEc:hhs:nhheco:2025_017 |
| By: | Mononen, Lasse (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | Models of choice under uncertainty study choice behavior when outcomes depend on the realized state of the world. The typical assumption is that utilities of outcomes do not depend on the realized state and are state independent. Without this simplifying assumption, it is difficult to separately identify utilities and beliefs. This paper provides novel general foundations for models with state dependent utilities: once we depart from expected utility, it is often possible to uniquely identify utilities and beliefs. Specifically, we show that with general models of non-expected utility under ambiguity we have complete identification of utilities and probabilities under full-dimensional uncertainty. Additionally, we offer novel axiomatizations for state dependent dual-self variational expected utility and dual-self expected utility. |
| Keywords: | State dependent utility, belief identification, ambiguity, multiple priors, dual-self expected utility |
| Date: | 2025–08–15 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:738 |
| By: | Mononen, Lasse (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We reconsider the foundations of expected utility without assuming the linearity of the independence axiom. We consider a decision-maker who cancels out common outcomes when comparing a pair of lotteries with the same probability tree. We show that if the decision-maker is consistent with first-order stochastic dominance or topological continuity in weak convergence, then the decision-maker is an expected utility maximizer. This offers a simple method to differentiate behavior between prospect theory, canceling out common outcomes in pairwise comparisons, and cumulative prospect theory, satisfying first-order stochastic dominance. Additionally, this offers a novel method to test technical continuity assumptions based on their behavioral content that rules out, e.g., prospect theory. |
| Keywords: | Expected utility, branch cancellation, first-order stochastic dominance, testing axioms, prospect theory, cumulative prospect theory |
| Date: | 2025–08–14 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:728 |
| By: | Leandro Gorno; Paulo Klinger Monteiro |
| Abstract: | This paper provides a general characterization of preferences that admit a Richter-Peleg representation without imposing completeness or transitivity. We establish that a binary relation on a nonempty set admits a Richter-Peleg representation if and only if it is "strongly acyclic" and its transitive closure is "separable". Strong acyclicity rules out problematic cycles among indifference classes, while separability limits the structural complexity of the relation. Our main result has two significant corollaries. First, when the set of alternatives is countable, a binary relation admits a Richter-Peleg representation if and only if it is strongly acyclic. Second, a preorder admits a Richter-Peleg representation if and only if it is separable. These findings have important implications for decision theory, particularly for obtaining maximal elements through scalar maximization in the presence of indecisiveness. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.08980 |
| By: | Joshua Zeitlin; Corinna Coupette |
| Abstract: | Whether the goal is to analyze voting behavior, locate facilities, or recommend products, the problem of translating between (ordinal) rankings and (numerical) utilities arises naturally in many contexts. This task is commonly approached by representing both the individuals doing the ranking (voters) and the items to be ranked (alternatives) in a shared metric space, where ordinal preferences are translated into relationships between pairwise distances. Prior work has established that any collection of rankings with $n$ voters and $m$ alternatives (preference profile) can be embedded into $d$-dimensional Euclidean space for $d \geq \min\{n, m-1\}$ under the Euclidean norm and the Manhattan norm. We show that this holds for all $p$-norms and establish that any pair of rankings can be embedded into $R^2$ under arbitrary norms, significantly expanding the reach of spatial preference models. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.09046 |
| By: | Cole Wyeth; Marcus Hutter; Jan Leike; Jessica Taylor |
| Abstract: | A Bayesian player acting in an infinite multi-player game learns to predict the other players' strategies if his prior assigns positive probability to their play (or contains a grain of truth). Kalai and Lehrer's classic grain of truth problem is to find a reasonably large class of strategies that contains the Bayes-optimal policies with respect to this class, allowing mutually-consistent beliefs about strategy choice that obey the rules of Bayesian inference. Only small classes are known to have a grain of truth and the literature contains several related impossibility results. In this paper we present a formal and general solution to the full grain of truth problem: we construct a class of strategies wide enough to contain all computable strategies as well as Bayes-optimal strategies for every reasonable prior over the class. When the "environment" is a known repeated stage game, we show convergence in the sense of [KL93a] and [KL93b]. When the environment is unknown, agents using Thompson sampling converge to play $\varepsilon$-Nash equilibria in arbitrary unknown computable multi-agent environments. Finally, we include an application to self-predictive policies that avoid planning. While these results use computability theory only as a conceptual tool to solve a classic game theory problem, we show that our solution can naturally be computationally approximated arbitrarily closely. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.16245 |
| By: | Edith Elkind; Tzeh Yuan Neoh; Nicholas Teh |
| Abstract: | We study a temporal voting model where voters have dynamic preferences over a set of public chores -- projects that benefit society, but impose individual costs on those affected by their implementation. We investigate the computational complexity of optimizing utilitarian and egalitarian welfare. Our results show that while optimizing the former is computationally straightforward, minimizing the latter is computationally intractable, even in very restricted cases. Nevertheless, we identify several settings where this problem can be solved efficiently, either exactly or by an approximation algorithm. We also examine the effects of enforcing temporal fairness and its impact on social welfare, and analyze the competitive ratio of online algorithms. We then explore the strategic behavior of agents, providing insights into potential malfeasance in such decision-making environments. Finally, we discuss a range of fairness measures and their suitability for our setting. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.08810 |
| By: | Beißner, Patrick (Center for Mathematical Economics, Bielefeld University); Werner, Jan (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | The analysis of optimal risk sharing has been thus far largely restricted to non-expected utility models with concave utility functions, where concavity is an expression of ambiguity aversion and/or risk aversion. This paper extends the analysis to $\alpha$-maxmin expected utility, Choquet expected utility, and Cumulative Prospect Theory, which accommodate ambiguity seeking and risk seeking attitudes. We introduce a novel methodology of quasidifferential calculus of Demyanov and Rubinov (1986, 1992) and argue that it is particularly well-suited for the analysis of these three classes of utility functions which are neither concave nor differentiable. We provide characterizations of quasidifferentials of these utility functions, derive first-order conditions for Pareto optimal allocations under uncertainty, and analyze implications of these conditions for risk sharing with and without aggregate risk. |
| Keywords: | quasidifferential calculus, ambiguity, Pareto optimality, $\alpha$-MaxMin expected utility, Choquet expected utility, rank-dependent expected utility, Cumulative Prospect Theory |
| Date: | 2025–07–18 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:722 |
| By: | Mononen, Lasse (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | Complexity aversion is well-documented in choice under risk. One of the main behavioral effects of complexity aversion is the event-splitting effect. This captures the change in the value of a lottery from splitting a prize of the lottery into two separate prizes by halving the probability. We relax the independence axiom for the event-splitting effect. Under continuity assumptions, this characterizes a decision-maker that is either 1) an expected utility maximizer with an entropic cost of complexity or 2) a powerweighted expected utility maximizer that weights probabilities by a power function. Additionally, our model offers preference foundations for the logit random choice. |
| Date: | 2025–08–18 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:748 |
| By: | Hideo Konishi (Boston College; National Chengchi University, Taiwan); Dimitar Simeonov (Bahçeşehir University) |
| Abstract: | In this paper, we formalize a market with a large number of competing production teams following Alchian and Demsetz (1974). We allow for wide-spread externalities which can affect players’ payoffs. These externalities include changes in market conditions and pollutions, and may generate a variety of equilibrium outcomes. There are finite types of atomless players, who can form team-firms with finite memberships using available technologies. Given an arbitrary set of feasible partnership contracts for each team type, we consider free entry equilibrium as our equilibrium concept—in a free entry equilibrium, no team type can attract its members from other teams by proposing any implementable partnership contract. Furthermore, in a free entry equilibrium, players of the same type may have different payoffs—unequal treatment of equals. We show that as long as each firm type’s implementable payoff set is compact and continuous in externality variables, there exists a free entry equilibrium. We provide several applications of our results. |
| Keywords: | competing teams, widespread externalities, unequal treatment of equals, free entry equilibrium, labor managed firms, coalition formation |
| JEL: | C71 C78 D2 D4 |
| Date: | 2025–08–21 |
| URL: | https://d.repec.org/n?u=RePEc:boc:bocoec:1095 |
| By: | Yasunori Okumura |
| Abstract: | This paper studies general multi-unit probabilistic assignment problems involving indivisible objects, with a particular focus on achieving the fundamental fairness notion known as equal treatment of equals (ETE) and ensuring various notions of efficiency. We extend the definition of ETE so that it accommodates a variety of constraints and applications. We analyze the ETE reassignment procedure, which transforms any assignment into one satisfying ETE, and examine its compatibility with three efficiency concepts: ex-post efficiency, ordinal efficiency, and rank-minimizing efficiency. We show that while the ETE reassignment of an ex-post efficient assignment remains ex-post efficient, it may fail to preserve ordinal efficiency in general settings. However, since the ETE reassignment of a rank-minimizing assignment preserves rank-minimizing efficiency, the existence of assignments satisfying both ETE and ordinal efficiency can be established. Furthermore, we propose a computationally efficient method for constructing assignments that satisfy both ETE and ordinal efficiency under general upper bound constraints, by combining the serial dictatorship rule with appropriately specified priority lists and an ETE reassignment. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.14522 |
| By: | Joy Das Bairagya; Sagar Chakraborty |
| Abstract: | Humans are bounded rational at best and this, we argue, has worked in their favour in the hunter-gatherer society where emergence of a coordinated action, leading to cooperation, is otherwise the standard stag-hunt dilemma (when individuals are rational). In line with the fact the humans strive for developing self-reputation by having less propensity to cheat than to be cheated, we observe that the payoff structure of the stag-hunt game appropriately modifies to that of coordination-II game. Subsequently, within the paradigm of evolutionary game theory, we establish that a population -- consisting of procedural rational players (a type of bounded rationality) -- is unequivocally evolutionarily stable against emergence of more rational strategies in coordination-II game. The cooperation is, thus, shown to have been established by evolutionary forces picking less rational individuals. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.08301 |
| By: | Asen Kochov |
| Abstract: | Recursive utility functions are often defined implicitly, as the solution of a functional equation known as the Koopmans recursion. As conditions for a unique solution can be demanding, a recent literature has tackled the problem of multiplicity, advocating that one focus attention on either the least or greatest solution, which possess a number of attractive properties. While a least solution can be shown to exist, I show that in the most general formulation of the problem, a greatest solution need not. The goal of the paper is to provide a sufficient condition for the existence of a greatest solution, which I term the weakly contractive property and which generalizes the usual contractive property sufficient for uniqueness. |
| Keywords: | recursive utility, greatest and lowest fixed point, contractions |
| JEL: | C6 D9 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_12091 |
| By: | Cesare Carissimo; Fryderyk Falniowski; Siavash Rahimi; Heinrich Nax |
| Abstract: | This paper proposes a fresh `meta-game' perspective on the problem of algorithmic collusion in pricing games a la Bertrand. Economists have interpreted the fact that algorithms can learn to price collusively as tacit collusion. We argue instead that the co-parametrization of algorithms -- that we show is necessary to obtain algorithmic collusion -- requires algorithm designer(s) to engage in explicit collusion by algorithm orchestration. To highlight this, we model a meta-game of algorithm parametrization that is played by algorithm designers, and the relevant strategic analyses at that level reveal new equilibrium and collusion phenomena. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.14766 |
| By: | Ali Aouad; Jingwei Ji; Yaron Shaposhnik |
| Abstract: | The Pandora's box problem (Weitzman 1979) is a core model in economic theory that captures an agent's (Pandora's) search for the best alternative (box). We study an important generalization of the problem where the agent can either fully open boxes for a certain fee to reveal their exact values or partially open them at a reduced cost. This introduces a new tradeoff between information acquisition and cost efficiency. We establish a hardness result and employ an array of techniques in stochastic optimization to provide a comprehensive analysis of this model. This includes (1) the identification of structural properties of the optimal policy that provide insights about optimal decisions; (2) the derivation of problem relaxations and provably near-optimal solutions; (3) the characterization of the optimal policy in special yet non-trivial cases; and (4) an extensive numerical study that compares the performance of various policies, and which provides additional insights about the optimal policy. Throughout, we show that intuitive threshold-based policies that extend the Pandora's box optimal solution can effectively guide search decisions. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.07508 |
| By: | Takashi Izumo |
| Abstract: | The St. Petersburg paradox presents a longstanding challenge in decision theory. It describes a game whose expected value is infinite, yet for which no rational finite stake can be determined. Traditional solutions introduce auxiliary assumptions, such as diminishing marginal utility, temporal discounting, or extended number systems. These methods often involve mathematical refinements that may not correspond to how people actually perceive or process numerical information. This paper explores an alternative approach based on a modified operation of addition defined over coarse partitions of the outcome space. In this model, exact numerical values are grouped into perceptual categories, and each value is replaced by a representative element of its group before being added. This method allows for a phenomenon where repeated additions eventually cease to affect the outcome, a behavior described as inertial stabilization. Although this is not intended as a definitive resolution of the paradox, the proposed framework offers a plausible way to represent how agents with limited cognitive precision might handle divergent reward structures. We demonstrate that the St. Petersburg series can become inert under this coarse addition for a suitably constructed partition. The approach may also have broader applications in behavioral modeling and the study of machine reasoning under perceptual limitations. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.12475 |
| By: | Steg, Jan-Henrik (Center for Mathematical Economics, Bielefeld University); Thijssen, Jacco J.J. (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We study strategic investment in continuous time with positive externalities of changing magnitude. Our model particularly allows for two correlated risk factors. Constructing subgame-perfect equilibria with pure and mixed strategies, we observe the novel effect that it is important for the firms to anticipate preemption. In fact, the presence of a second risk factor implies also an additional strategic risk. We quantify the associated extra waiting cost and show that it is ex ante uncertain whether investment will happen when there is a first- or a second-mover advantage. Our formal arguments involve several methodological contributions. In addition, we provide detailed specifications of our basic model to address various applications. |
| Keywords: | Real options, Externalities, Preemption, War of attrition, Optimal stopping, Multidimensional |
| Date: | 2025–07–03 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:708 |
| By: | Patrick Lederer |
| Abstract: | In rank aggregation, the task is to aggregate multiple weighted input rankings into a single output ranking. While numerous methods, so-called social welfare functions (SWFs), have been suggested for this problem, all of the classical SWFs tend to be majoritarian and are thus not acceptable when a proportional ranking is required. Motivated by this observation, we will design SWFs that guarantee that every input ranking is proportionally represented by the output ranking. Specifically, our central fairness condition requires that the number of pairwise comparisons between candidates on which an input ranking and the output ranking agree is proportional to the weight of the input ranking. As our main contribution, we present a simple SWF called the Proportional Sequential Borda rule, which satisfies this condition. Moreover, we introduce two variants of this rule: the Ranked Method of Equal Shares, which has a more utilitarian flavor while still satisfying our fairness condition, and the Flow-adjusting Borda rule, which satisfies an even stronger fairness condition. Many of our axioms and techniques are inspired by results on approval-based committee voting and participatory budgeting, where the concept of proportional representation has been studied in depth. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.16177 |