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on Game Theory |
| 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: | Riedel, Frank (Center for Mathematical Economics, Bielefeld University); Torrente, Maria-Laura (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | Berge equilibrium offers an alternative to Nash equilibrium in game theory, emphasizing coop- erative stability rather than individual optimization. Despite recent interest, a systematic study of Berge equilibria in finite normal form games is still lacking, with fundamental questions like existence remaining open. This paper characterizes Berge equilibria through a polynomial system of equa- tions, enabling computational algebra and algebraic geometry methods to analyze them. Algorithms based on Gröbner bases determine the existence and computation of Berge equilibria. Furthermore, we show that the set of games admitting completely mixed Berge equilibria is contained within a determinantal variety, whose dimension we explicitly bound from above. |
| Keywords: | Berge equilibrium, Algebraic Methods in Economics, Gröbner Bases |
| Date: | 2025–07–22 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:750 |
| 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: | 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: | 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: | 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: | Leizerman, Samuel L |
| Abstract: | This paper rigorously proves that Unified Cognitive Field Theory (UCFT) provides a fundamental, non-Markovian game-theoretic framework for cognition. I demonstrate that the seven core UCFT operators and field dynamics are necessary and sufficient to represent all cognitive game-theoretic phenomena, establishing a precise isomorphism between the evolution of the cognitive field and strategic dynamics. This framework explicitly accounts for history-dependent processes, offering a novel perspective on the physics of learning and the emergence of cognitive biases. A key implication explored is the concept of “Learning as a Solitaire Self-Game, ” where individual cog- nition is viewed as a strategic optimization process against internal uncertainties, governed by substrate-dependent physical constants. This unification provides powerful new tools for understanding the complex interplay between physical substrate, strategic interaction, and the non-Markovian nature of intelligence. Keywords: non-Markovian game theory, cognitive field theory, quantum cognition, strategic dynamics, learning physics, cognitive bias, helical fiber bundles, substrate-dependent cognition, self-play optimization, temporal game theory, field-theoretic neuroscience, consciousness as strategy, memory persistence, cognitive temperature, strategic noise cancelling, belief revision dynamics, UCFT operators, Nash equilibria in cognitive space, Bayesian field updates, angle of attack learning This is an early draft and an excerpt from a larger monograph that will be posted later; this proof has some dependencies on that which are not explicitly proven because they are proven there. Furthermore, expect this to be updated. Commercial software implementations are patent pending (63/849, 479), but academics and researchers are welcomed and encouraged to use freely if this proves accurate. |
| Date: | 2025–08–05 |
| URL: | https://d.repec.org/n?u=RePEc:osf:socarx:hxfp9_v1 |
| 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: | Arunava Patra; Supratim Sengupta; Sagar Chakraborty |
| Abstract: | Learning from experience is a key feature of decision-making in cognitively complex organisms. Strategic interactions involving Bayesian inferential strategies can enable us to better understand how evolving individual choices to be altruistic or selfish can affect collective outcomes in social dilemmas. Bayesian strategies are distinguished, from their reactive opponents, in their ability to modulate their actions in the light of new evidence. We investigate whether such strategies can be resilient against reactive strategies when actions not only determine the immediate payoff but can affect future payoffs by changing the state of the environment. We use stochastic games to mimic the change in environment in a manner that is conditioned on the players' actions. By considering three distinct rules governing transitions between a resource-rich and a resource-poor states, we ascertain the conditions under which Bayesian tit-for-tat strategy can resist being invaded by reactive strategies. We find that the Bayesian strategy is resilient against a large class of reactive strategies and is more effective in fostering cooperation leading to sustenance of the resource-rich state. However, the extent of success of the Bayesian strategies depends on the other strategies in the pool and the rule governing transition between the two different resource states. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.00363 |
| By: | Dylan Laplace Mermoud; Michel Grabisch; Peter Sudh\"olter |
| Abstract: | Minimal balanced collections are a generalization of partitions of a finite set of n elements and have important applications in cooperative game theory and discrete mathematics. However, their number is not known beyond n = 4. In this paper we investigate the problem of generating minimal balanced collections and implement the Peleg algorithm, permitting to generate all minimal balanced collections till n = 7. Secondly, we provide practical algorithms to check many properties of coalitions and games, based on minimal balanced collections, in a way which is faster than linear programming-based methods. In particular, we construct an algorithm to check if the core of a cooperative game is a stable set in the sense of von Neumann and Morgenstern. The algorithm implements a theorem according to which the core is a stable set if and only if a certain nested balancedness condition is valid. The second level of this condition requires generalizing the notion of balanced collection to balanced sets. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.05898 |
| 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: | Xue Dong He; Chen Yang; Yutian Zhou |
| Abstract: | Decentralized exchanges (DEXs) are alternative venues to centralized exchanges (CEXs) for trading cryptocurrencies and have become increasingly popular. An arbitrage opportunity arises when the exchange rate of two cryptocurrencies in a DEX differs from that in a CEX. Arbitrageurs can then trade on the DEX and CEX to make a profit. Trading on the DEX incurs a gas fee, which determines the priority of the trade being executed. We study a gas-fee competition game between two arbitrageurs who maximize their expected profit from trading. We derive the unique symmetric mixed Nash equilibrium and find that (i) the arbitrageurs may choose not to trade when the arbitrage opportunity and liquidity is small; (ii) the probability of the arbitrageurs choosing a higher gas fee is lower; (iii) the arbitrageurs pay a higher gas fee and trade more when the arbitrage opportunity becomes larger and when liquidity becomes higher; (iv) the arbitrageurs' expected profit could increase with arbitrage opportunity and liquidity. The above findings are consistent with our empirical study. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.08302 |
| By: | Alicia Mascare\~nas-Pazos; Silvia Lorenzo-Freire; Jose Maria Alonso-Meijide |
| Abstract: | Within the domain of game theory, power indexes are defined as functions that quantify the influence of individual participants in collective decision-making processes. Felsenthal [D. Felsenthal. A Well-Behaved Index of a Priori P-Power for Simple N-Person Games. Homo Oeconomicus, 33, 2016] proposed a power index with a focus on least size winning coalitions, i.e., those coalitions capable of determining the final outcome and with the smallest number of players among all winning coalitions. However, the Felsenthal index overlooks pre-existing affinities between the players, a common and impactful factor in real-world political and economic contexts. This paper introduces the Felsenthal Owen power index, a novel index based on Felsenthal's approach that integrates player affinities using Owen's a priori unions framework. The new index is rigorously characterised by two distinct sets of axiomatic properties. We demonstrate its practical utility by applying it to the International Monetary Fund's voting system, revealing how strategic alliances significantly reshape power distributions. The index thus offers policymakers a more sophisticated tool for measuring influence in complex decision-making scenarios. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.01621 |
| By: | Encarnación Algaba (IMUS - Matematica Aplicada II and Instituto de Matematicas de la Universidad de Sevilla (IMUS), Escuela Superior de Ingenieros, Camino de los Descubrimientos, s/n, 41092 Sevilla, Spain); Eric Rémila (GATE-LSE - Université de Saint-Etienne, UMR CNRS GATE Lyon-St-Etienne UMR 5824, F-42023 Saint- Etienne Institution GATE-LSEFrance); Philippe Solal (GATE-LSE - Université de Saint-Etienne, UMR CNRS GATE Lyon-St-Etienne UMR 5824, F-42023 Saint- Etienne) |
| Abstract: | A cooperative games with a coalition structure is formed by a TUgame and a partition of the agent set. For this class of games, the Owen value is computed as a two-step procedure where the relevant coalitions are those formed by the union of some elements of the partition and a coalition of another element of the partition. In this paper, we consider a broader class of games where the partition is replaced by a collection of (not necessarily pairwise disjoint) coalitions over the agent set and where, in each element of this collection, cooperation among the agents is restricted. Agents then organize themselves into a profile of feasible coalitions. This class of games can be applied to several situations such as the problem of allocating aircraft landing fees in the presence of airlines and codeshare flights. We begin by defining and axiomatically characterizing the class of flow methods, which are marginal values whose coefficients induce a unit flow on the graph of feasible coalition profiles. We then define Owen-type values constructed from flow methods. We show that these values are flow methods whose flow is decomposable into two flows. Finally, we introduce two axioms from which we characterize the flows that can be decomposed in this way, and hence the flow methods constructed by our Owen-type procedure. The last part of the paper studies some special cases. |
| Keywords: | Coalition configuration Cooperative games Flow Set systems Marginalist values Airport games Mathematics Subject Classification (2000) 91A12 91A43 05C21, Coalition configuration, Cooperative games, Flow, Set systems, Marginalist values, Airport games Mathematics Subject Classification (2000) 91A12, 91A43, 05C21 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:halshs-05164853 |
| By: | Conzo, Pierluigi (University of Turin); Della Giusta, Marina (University of Turin); Dubois, Florent (University of Torino); Rosso, Giacomo (University of Turin); Razzu, Giovanni (University of Reading) |
| Abstract: | Mental health is vital for well-being and productivity, yet investment remains chronically low. We study how different framings of mental health investment affect cooperation and donations using a pre-registered online experiment across five European countries (N = 8, 312). Participants were randomly assigned to receive information emphasizing either individual benefits (Private Perspective), collective benefits (Public Perspective), or prevalence data (Neutral Perspective). All treatments significantly increase cooperation in a Public Goods Game and donations in a Charity Dictator Game, suggesting intrinsic motivation drives behavior. Only the Private Perspective increases personal normative expectations, while empirical expectations remain unaffected—suggesting that interventions influence moral beliefs more than beliefs about others’ actions. All treatments reduce self-reported mental health stigma, consistent with evidence from a list experiment, suggesting stigma reduction as a key mechanism. Heterogeneity analyses show stronger treatment effects among individuals with lived experience or prior concern, and reduced contributions under collective framings when public provision is perceived as adequate—consistent with a substitution effect between public and private action. Donations also decline in post- communist countries, aligning with historically lower institutional trust and weaker norms of private giving. These findings highlight how individual perceptions and institutional legacies shape behavioural responses, and suggest that perceived adequacy of public provision can backfire by discouraging private engagement—potentially trapping societies in a bad equilibrium of persistent underinvestment in mental health. |
| Keywords: | online survey experiment, stigma, donations, cooperation, mental health, information treatment |
| JEL: | C90 I12 I18 I31 |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:iza:izadps:dp18054 |
| By: | Marta C. Couto; Flavia Barsotti; Fernando P. Santos |
| Abstract: | Classification algorithms based on Artificial Intelligence (AI) are nowadays applied in high-stakes decisions in finance, healthcare, criminal justice, or education. Individuals can strategically adapt to the information gathered about classifiers, which in turn may require algorithms to be re-trained. Which collective dynamics will result from users' adaptation and algorithms' retraining? We apply evolutionary game theory to address this question. Our framework provides a mathematically rigorous way of treating the problem of feedback loops between collectives of users and institutions, allowing to test interventions to mitigate the adverse effects of strategic adaptation. As a case study, we consider institutions deploying algorithms for credit lending. We consider several scenarios, each representing different interaction paradigms. When algorithms are not robust against strategic manipulation, we are able to capture previous challenges discussed in the strategic classification literature, whereby users either pay excessive costs to meet the institutions' expectations (leading to high social costs) or game the algorithm (e.g., provide fake information). From this baseline setting, we test the role of improving gaming detection and providing algorithmic recourse. We show that increased detection capabilities reduce social costs and could lead to users' improvement; when perfect classifiers are not feasible (likely to occur in practice), algorithmic recourse can steer the dynamics towards high users' improvement rates. The speed at which the institutions re-adapt to the user's population plays a role in the final outcome. Finally, we explore a scenario where strict institutions provide actionable recourse to their unsuccessful users and observe cycling dynamics so far unnoticed in the literature. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.09340 |
| By: | Banas, Lubomir (Center for Mathematical Economics, Bielefeld University); Ferrari, Giorgio (Center for Mathematical Economics, Bielefeld University); Randrianasolo, Tsiry Avisoa (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We propose an implementable, neural network-based structure preserving probabilistic numerical approximation for a generalized obstacle problem describing the value of a zero-sum differential game of optimal stopping with asymmetric information. The target solution depends on three variables: the time, the spatial (or state) variable, and a variable from a standard (I - 1)-simplex which represents the probabilities with which the I possible configurations of the game are played. The proposed numerical approximation preserves the convexity of the continuous solution as well as the lower and upper obstacle bounds. We show convergence of the fully-discrete scheme to the unique viscosity solution of the continuous problem and present a range of numerical studies to demonstrate its applicability. |
| Date: | 2025–08–14 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:733 |
| By: | Sophie Clot (EDHEC - EDHEC Business School - UCL - Université catholique de Lille); Gilles Grolleau (ESSCA - ESSCA – École supérieure des sciences commerciales d'Angers = ESSCA Business School); Lisette Ibanez (CEE-M - Centre d'Economie de l'Environnement - Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - UM - Université de Montpellier) |
| Abstract: | This study investigates the extent to which people are subject to moral licensing in the environmental domain by examining moral dynamics at a disaggregated level. Using Giving and Taking games with environmental NGOs, we found that aggregate results hide important heterogeneity. Half of the participants engaged in compensatory behavior, with highly environmentally concerned individuals compensating more frequently. Men were more consistent than women, but when they adopted moral licensing, their compensation was significantly greater than that of women. These findings suggest opportunities for improving environmental policy effectiveness. |
| Keywords: | taking game, moral in(consistency), licensing, dictator game, cleansing |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-05148018 |
| By: | Dingyi Wang; Ruqiang Guo; Qian Lu |
| Abstract: | The promotion of Conservation Tillage Technology (CTT) is critical for mitigating global soil degradation, yet their actual adoption rates remain substantially lower than anticipated targets. Existing research predominantly focuses on static factor analyses, failing to adequately capture the dynamic evolutionary mechanisms of farmer strategic interactions and the impacts of information asymmetries in agricultural markets. This study constructs an evolutionary game model integrating heterogeneous time preferences and lemon market effects to reveal the dynamic equilibrium of technology adoption within farmer groups operating under bounded rationality. Key findings indicate that farmers with high time preferences significantly impede CTT adoption due to the excessive discounting of long-term benefits. Furthermore, the lemon market effect dictates the system's equilibrium states: 1) When the lemon market benefit ($P$) exceeds the lemon market loss ($Q$) ($P > Q$), stable tripartite coexistence of adoption strategies emerges; 2) When $P |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.15497 |
| By: | Agustin G. Bonifacio; Maria Haydee Fonseca-Mairena; Pablo Neme |
| Abstract: | We study coalition formation problems in the presence of externalities, focusing on settings where agents exhibit myopic expectations, that is, they evaluate potential deviations based solely on the immediate outcome, assuming no further reactions or reorganization by others. First, we establish a sufficient condition for the non-emptiness of both the core and the stable set. In the case of the core, our condition for ensuring non-emptiness also provides a characterization of all core partitions. We then turn our attention to problems with order-preserving preferences. Under our sufficient condition, the core and the stable set not only exist but also coincide, and convergence to a stable outcome is guaranteed. Furthermore, using the notion of absorbing set, we draw a connection between problems with order-preserving preferences and those without externalities. This allows us to lift known core non-emptiness results from the latter setting to the former, thereby establishing a novel bridge between these two classes of problems. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.03259 |
| 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: | 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: | T\'imea Kov\'acs; D\'ora Gr\'eta Petr\'oczy; G\'abor P\'asztor |
| Abstract: | As of 2022, the European Union has taken several steps regarding enlargement. We focus on the accession of countries with which the Union is actively negotiating membership. This is examined under two enlargement scenarios: first, the enlargement along the lines of the Western Balkan countries, and second, the accession of a trio (Ukraine, Moldova, and Georgia) to the already enlarged Union. We determine the a priori power of the member states based on the Banzhaf and Shapley--Shubik indices. Various coalitions are also assumed to assess the power and influence of member states, considering both pre- and post-enlargement scenarios. We found a rare case when the two indices give different rankings. In the case of the Western Balkan countries' accession, the smaller population member states gain power, presenting an example of the new member paradox. While in a Union of 36 members, every member state loses some of their current power. However, some coalitions are better off with the EU36 enlargement than a EU33 one. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.08914 |
| By: | Athanasios Andrikopoulos; Nikolaos Sampanis |
| Abstract: | The theory of optimal choice sets offers a well-established solution framework in social choice and game theory. In social choice theory, decision-making is typically modeled as a maximization problem. However, when preferences are cyclic -- as can occur in economic processes -- the set of maximal elements may be empty, raising the key question of what should be considered a valid choice. To address this issue, several approaches -- collectively known as general solution theories -- have been proposed for constructing non-empty choice sets. Among the most prominent in the context of a finite set of alternatives are the Stable Set (also known as the Von Neumann-Morgenstern set) and its extensions, such as the Extended Stable Set, the socially stable set, and the $m$-, and $w$-stable sets. In this paper, we extend the classical concept of the stable set and its major variants - specifically, the extended stable set, the socially stable set, and the $m$- and $w$-stable sets - within the framework of irreflexive binary relations over infinite sets of alternatives. Additionally, we provide a topological characterization for the existence of such general solutions. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.09798 |