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on Game Theory |
| By: | Gaëtan Fournier (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique); Eden Kuperwasser (TAU - Tel Aviv University); Orin Munk (TAU - Tel Aviv University); Eilon Solan (TAU - Tel Aviv University); Avishay Weinbaum (TAU - Tel Aviv University) |
| Abstract: | We study approachability theory in the presence of constraints. Given a repeated game with vector payoffs, we study the pairs of sets (A, D) in the payoff space such that Player 1 can guarantee that the long-run average payoff converges to the set A, while the average payoff always remains in D. We provide a full characterization of these pairs when D is convex and open, and a sufficient condition when D is not convex. |
| Keywords: | game theory, approachability, optimization |
| Date: | 2021–07 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03138536&r=gth |
| By: | Guanxing Fu; Paul P. Hager; Ulrich Horst |
| Abstract: | We consider a novel class of portfolio liquidation games with market drop-out ("absorption"). More precisely, we consider mean-field and finite player liquidation games where a player drops out of the market when her position hits zero. In particular round-trips are not admissible. This can be viewed as a no statistical arbitrage condition. In a model with only sellers we prove that the absorption condition is equivalent to a short selling constraint. We prove that equilibria (both in the mean-field and the finite player game) are given as solutions to a non-linear higher-order integral equation with endogenous terminal condition. We prove the existence of a unique solution to the integral equation from which we obtain the existence of a unique equilibrium in the MFG and the existence of a unique equilibrium in the $N$-player game. We establish the convergence of the equilibria in the finite player games to the obtained mean-field equilibrium and illustrate the impact of the drop-out constraint on equilibrium trading rates. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.05783&r=gth |
| By: | Roberto Corrao; Yifan Dai |
| Abstract: | We study optimal (information) mediation in sender-receiver communication games where the sender has transparent motives: she only cares about the receiver's actions and beliefs. We characterize the feasible distributions over the receiver's beliefs under mediation and the value of mediation. The sender achieves her optimal Bayesian persuasion value by mediation if and only if this value is attained by cheap talk. When the state is binary, mediation strictly improves on cheap talk if and only if the sender cannot do better than under cheap talk by always under -- or over -- stating the state. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.06244&r=gth |
| By: | Furkan Sezer; Ceyhun Eksin |
| Abstract: | Information design in an incomplete information game includes a designer with the goal of influencing players' actions through signals generated from a designed probability distribution so that its objective function is optimized. If the players have quadratic payoffs that depend on the players' actions and an unknown payoff-relevant state, and signals on the state that follow a Gaussian distribution conditional on the state realization, then the information design problem under quadratic design objectives is a semidefinite program (SDP). We consider a setting in which the designer has partial knowledge on agents' utilities. We address the uncertainty about players' preferences by formulating a robust information design problem. Specifically, we consider ellipsoid perturbations over payoff matrices in linear-quadratic-Gaussian (LQG) games. We show that this leads to a tractable robust SDP formulation. Using the robust SDP formulation, we obtain analytical conditions for the optimality of no information and full information disclosure. The robust convex program is also extended to interval and general convex cone uncertainty sets on the payoff matrices. Numerical studies are carried out to identify the relation between the perturbation levels and the optimal information structures. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.05489&r=gth |
| By: | Anastasiya Tanana |
| Abstract: | We consider existence and uniqueness of Nash equilibria in an $N$-player game of utility maximization under relative performance criteria of multiplicative form in complete semimartingale markets. For a large class of players' utility functions, a general characterization of Nash equilibria for a given initial wealth vector is provided in terms of invertibility of a map from $\mathbb{R}^N$ to $\mathbb{R}^N$. As a consequence of the general theorem, we derive existence and uniqueness of Nash equilibria for an arbitrary initial wealth vector, as well as their convergence, if either (i) players' utility functions are close to CRRA, or (ii) players' competition weights are small and relative risk aversions are bounded away from infinity. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.07941&r=gth |
| By: | Fakhrabadi, Mahnaz (Dept. of Business and Management Science, Norwegian School of Economics); Sandal, Leif K. (Dept. of Business and Management Science, Norwegian School of Economics) |
| Abstract: | This paper investigates a multi-periodic channel optimization facing uncertain, price dependent, and dynamic demand. The picture of the market uncertainty is incomplete, and only the price and time-dependent mean and standard deviation are known and may depend on the price history. The actual demand distribution itself is unknown as is typically the case in real world problems. An algorithm finding the optimized decentralized channel equilibrium is developed when the downstream member optimizes her expected profit stream by a distributional-robust approach, and the upstream member (leader) considers it as the follower’s reaction function. The algorithm allows for strategic decisions whereby the current demand is scaled by the previous price setting. |
| Keywords: | Multi-Periodic problem; Stochasticity; Stackelberg Game; Subgame Perfect Distributional-Robust Approach; Supply Chain Management; Price-History Dependent Dynamic Demand |
| JEL: | C61 C62 C63 C72 C73 D81 |
| Date: | 2023–03–22 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:nhhfms:2023_004&r=gth |
| By: | Chowdhury Mohammad Sakib Anwar; Jorge Bruno; Renaud Foucart; Sonali SenGupta |
| Abstract: | We model a public goods game with groups, position uncertainty, and observational learning. Contributions are simultaneous within groups, but groups play sequentially based on their observation of an incomplete sample of past contributions. We show that full cooperation between and within groups is possible with self-interested players on a fixed horizon. Position uncertainty implies the existence of an equilibrium where groups of players conditionally cooperate in the hope of influencing further groups. Conditional cooperation implies that each group member is pivotal, so that efficient simultaneous provision within groups is an equilibrium. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.10514&r=gth |
| By: | Mao Fabrice Djete; Gaoyue Guo; Nizar Touzi |
| Abstract: | We introduce the possibility of default in the mean field game of mutual holding of Djete and Touzi [11]. This is modeled by introducing absorption at the origin of the equity process. We provide an explicit solution of this mean field game. Moreover, we provide a particle system approximation, and we derive an autonomous equation for the time evolution of the default probability, or equivalently the law of the hitting time of the origin by the equity process. The systemic risk is thus described by the evolution of the default probability. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.07996&r=gth |
| By: | Anton V. Proskurnikov; B. Ross Barmish |
| Abstract: | The takeoff point for this paper is the voluminous body of literature addressing recursive betting games with expected logarithmic growth of wealth being the performance criterion. Whereas almost all existing papers involve use of linear feedback, the use of nonlinear control is conspicuously absent. This is epitomized by the large subset of this literature dealing with Kelly Betting. With this as the high-level motivation, we study the potential for use of nonlinear control in this framework. To this end, we consider a ``demonstration case'' which is one of the simplest scenarios encountered in this line of research: repeated flips of a biased coin with probability of heads~$p$ and even-money payoff on each flip. First, we formulate a new robust nonlinear control problem which we believe is both simple to understand and apropos for dealing with concerns about distributional robustness; i.e., instead of assuming that~$p$ is perfectly known as in the case of the classical Kelly formulation, we begin with a bounding set for this probability. Then, we provide a theorem, our main result, which gives a closed-form description of the optimal robust nonlinear controller and a corollary which establishes that it robustly outperforms linear controllers such as those found in the literature. A second contribution of this paper bears upon the computability of our solution. For an $n$-flip game, whereas an admissible controller has~$2^n-1$ parameters, at the optimum only~$O(n^2)$ of them turn out to be distinct. Finally, we provide some illustrations comparing robust performance with what is possible when working with the so-called perfect-information Kelly optimum. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.10417&r=gth |
| By: | Didier Laussel (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique); Ngo van Long (Department of Economics [McGill University] - McGill University = Université McGill [Montréal, Canada], Hitotsubashi Institute for Advanced Study); Joana Resende (Cef.up, Economics Department, University of Porto) |
| Abstract: | A durable good monopolist faces a continuum of heterogeneous customers who make purchase decisions by comparing present and expected price-quality offers. The monopolist designs a sequence of price-quality menus to segment the market. We consider the Markov perfect equilibrium (MPE) of a game where the monopolist is unable to commit to future price-quality menus. We obtain the novel results that: (a) under certain conditions, the monopolist covers the whole market in the first period (even when a static Mussa–Rosen monopolist would not cover the whole market), because this is a strategic means to convince customers that lower prices would not be offered in future periods and that (b) this can happen only under the stage-wise Stackelberg leadership assumption (whereby consumers base their expectations on the value of the state variable at the end of the period). Conditions under which MPE necessarily involves sequentially trading are also derived. |
| Keywords: | Product quality, Durable good monopoly, Second-degree price discrimination, Coase conjecture |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03434362&r=gth |
| By: | Cortelyou C. Kenney |
| Abstract: | Classical law and economics is foundational to the American legal system. Centered at the University of Chicago, its assumptions, most especially that humans act both rationally and selfishly, informs the thinking of legislatures, judges, and government lawyers, and has shaped nearly every aspect of the way commercial transactions are conducted. But what if the Chicago School, as I refer to this line of thinking, is wrong? Alternative approaches such as behavioral law and economics or law and political economy contend that human decisionmaking is based on emotions or should not be regulated as a social geometry of bargains. This Article proposes a different and wholly novel reason that the Chicago School is wrong: a fundamental assumption central to many of its game theory models has been disproven. This Article shows that a 2012 breakthrough from world famous physicist Freeman Dyson shocked the world of game theory. This Article shows that Chicago School game theorists are wrong on their own terms because these 2 x 2 games such as the Prisoner's Dilemma, Chicken, and Snowdrift, ostensibly based on mutual defection and corrective justice, in fact yield to an insight of pure cooperation. These new game theory solutions can be scaled to design whole institutions and systems that honor the pure cooperation insight, holding out the possibility of cracking large scale social dilemmas like the tragedy of the commons. It demonstrates that, in such systems, pure cooperation is the best answer in the right environment and in the long run. It ends by calling for a new legal field to redesign the structures based on the outdated assumptions of the Chicago School game theorists. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.09321&r=gth |
| By: | Andrzej Baranski; Ernesto Reuben (Division of Social Science) |
| Abstract: | Competition for positions of power is a common practice in most organizations where decisions are reached through negotiations. We study theoretically and experimentally how different voting rules affect the incentives to compete for the right to propose a distribution of benefits in a sequential bargaining game. Under the majority rule, players with a high chance of proposing are also more likely to be excluded from a coalition when not proposing, which dampens incentives to compete for proposal rights relative to the unanimity case where no one can be excluded from a coalition. However, when rent-seeking efforts affect proposal rights only in the first bargaining round, equilibrium efforts to secure proposal rights are higher under the majority rule because they no longer affect the likelihood of coalition exclusion. Our experimental findings uncover a novel efficiency trade-off absent in theory: While gridlock is stronger under unanimity, majoritarian bargaining elicits higher competition costs regardless of the durability of efforts in affecting proposal rights, rendering both rules equally efficient. The distribution of benefits is affected by the endogeneity of proposal rights contrary to behavioral expectations as subjects gravitate towards equitable sharing and proposers often do not keep the lion’s share. Further experiments reveal that subject behavior is consistent with myopic reasoning and that our results hold robustly in distinct subject samples. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:nad:wpaper:20220085&r=gth |
| By: | Ngoc Thao NOET (GRANEM - Groupe de Recherche Angevin en Economie et Management - UA - Université d'Angers - Institut Agro Rennes Angers - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement); Marianne Lefebvre (GRANEM - Groupe de Recherche Angevin en Economie et Management - UA - Université d'Angers - Institut Agro Rennes Angers - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement); Serge Blondel (LIRAES (URP_ 4470) - Laboratoire Interdisciplinaire de Recherche Appliquée en Economie de la Santé - UPCité - Université Paris Cité, GRANEM - Groupe de Recherche Angevin en Economie et Management - UA - Université d'Angers - Institut Agro Rennes Angers - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement) |
| Abstract: | Through a field experiment based on the prisoner's dilemma, we analyze the determinants of cooperative behavior in the horticultural sector, specifically on the effect of group membership. We focus on the Flowers for Bees Week initiative, a collective action in the supply chain (in particular producers and landscapers). We compare the behaviors of professionals in a repeated prisoner's dilemma game over 5 days, in two treatments: in-group (the players have the same role in the sector) and out-group (one player is a producer and the other a landscaper). The results are threefold. First, cooperation is higher in the in-group treatment compared to the out-group treatment. Second, when they cooperate, it is because they believe that the other will also cooperate. Lastly, the two sectors share the same views on collective actions and cooperation. We suggest levers to encourage collective actions in the sector. |
| Keywords: | Cooperation, Field experiment, In-group Out-group effect, Horticulture, Prisoner's dilemma |
| Date: | 2023–02–25 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-04004727&r=gth |
| By: | C\'esar Barilla; Duarte Gon\c{c}alves |
| Abstract: | We study a model in which two players with opposing interests try to alter a status quo through instability-generating actions. We show that instability can be used to secure longer-term durable changes, even if it is costly to generate and does not generate short-term gains. In equilibrium, instability generated by a player decreases when the status quo favors them more. Equilibrium always exhibits a region of stable states in which the status quo persists. As players' threat power increases, this region shrinks, ultimately collapsing to a single stable state that is supported via a deterrence mechanism. There is long-run path-dependency and inequity: although instability eventually leads to a stable state, it typically selects the least favorable one for the initially disadvantaged player. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.07285&r=gth |
| By: | Manuel Foerster (Bielefeld University); Daniel Habermacher (Universidad de los Andes, Chile) |
| Abstract: | We investigate competition between experts with different motives. A policy-maker has to implement a policy and can either acquire information herself or hire a biased but well-informed expert. We show that the expertcharges a fee if interests between the agents are roughly aligned, and pays contributions in order to get the decision delegated—and thus acts as a lobbyist instead of as an advisor—if the conflict of interest is substantial and the policy is important to her. We then introduce an unbiased careerconcerned expert and show that lobbying may occur because of competition. Finally, the effect of competition on societal welfare may be negative if policy is (not) important to society but the unbiased expert provides bad (good) advice. |
| Keywords: | Policy advice, private information, delegation, lobbying, competition |
| JEL: | C72 D72 D82 D83 |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:aoz:wpaper:229&r=gth |
| By: | Adam Dominiak; Matthew Kovach; Gerelt Tserenjigmid |
| Abstract: | We introduce and characterize inertial updating of beliefs. Under inertial updating, a decision maker (DM) chooses a belief that minimizes the subjective distance between their prior belief and the set of beliefs consistent with the observed event. Importantly, by varying the subjective notion of distance, inertial updating provides a unifying framework that nests three different types of belief updating: (i) Bayesian updating, (ii) non-Bayesian updating rules, and (iii) updating rules for events with zero probability, including the conditional probability system (CPS) of Myerson (1986a, b). We demonstrate that our model is behaviorally equivalent to the Hypothesis Testing model (HT) of Ortoleva (2012), clarifying the connection between HT and CPS. We apply our model to a persuasion game. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.06336&r=gth |
| By: | Bontemps, Christian; Gualdani, Cristina; Remmy, Kevin |
| Abstract: | We develop a two-stage game in which competing airlines first choose the networks of markets to serve in the first stage before competing in price in the second stage. Spillovers in entry decisions across markets are allowed, which accrue on the demand, marginal cost, and fixed cost sides. We show that the second-stage parameters are point identified, and we design a tractable procedure to set identify the first-stage parameters and to conduct inference. Further, we estimate the model using data from the domestic US airline market and find significant spillovers in entry. In a counterfactual exercise, we evaluate the 2013 merger between American Airlines and US Airways. Our results highlight that spillovers in entry and post-merger network readjustments play an important role in shaping post-merger outcomes. |
| Keywords: | Endogenous market structure; Networks; Airlines; Oligopoly; Product repositioning; Mergers; Remedies |
| Date: | 2023–03–09 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:127943&r=gth |
| By: | Alejandro Esteller-Moré (Universitat de Barcelona & IEB); Umberto Galmarini (Università dell’Insubria & IEB) |
| Abstract: | In a two-country model, the citizens of a ‘big home country’ can either fictitiously move residence to a ‘small foreign country’ where residence-based taxes are lower (external tax avoidance), or under-report the tax base at home (internal tax avoidance). Tax setting is the result of Cournot-Nash competition between revenue maximizing governments, with the home government also setting two types of administration policies, one for each form of tax avoidance. We show that although it is optimal to employ both types of administration policies, which in themselves are both effective at tackling the targeted form of tax avoidance, the optimum is characterized by a tradeoff in terms of policy outcomes: either internal avoidance increases and external avoidance decreases, or the opposite, depending on the characteristics of the fiscal environment. |
| Keywords: | Personal taxation; Residence principle; Tax avoidance; Tax competition; Tax administration; Tax havens; Taxation of the rich; Leviathan governments |
| JEL: | H21 H24 H26 H73 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ieb:wpaper:doc2023-03&r=gth |
| By: | Marcus C Christiansen |
| Abstract: | A common problem in various applications is the additive decomposition of the output of a function with respect to its input variables. Functions with binary arguments can be axiomatically decomposed by the famous Shapley value. For the decomposition of functions with real arguments, a popular method is the pointwise application of the Shapley value on the domain. However, this pointwise application largely ignores the overall structure of functions. In this paper, axioms are developed which fully preserve functional structures and lead to unique decompositions for all Borel measurable functions. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.07773&r=gth |
| By: | Guillaume Monchambert (LAET - Laboratoire Aménagement Économie Transports - UL2 - Université Lumière - Lyon 2 - ENTPE - École Nationale des Travaux Publics de l'État - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | This paper investigates pricing decisions when a monopolistic multi-sided platform is myopic, that is unable to distinguish between two agents who participate on the same side of the platform but produce different externalities. We find that the structure of prices is the same for profit- and welfare-maximizing platforms. The unique price supplied to the two undistinguishable agents is a weighted average of the perfect information prices, where the weights depend on demand elasticities and externalities produced by the other undistinguishable agent. The prices supplied to the distinguishable agents are also affected by information asymmetry through an extra term than can be positive or negative. Introducing Hotelling competition does not affect results. We apply the model to a monopolistic short-distance carpooling platform with and without HOV lane, and show that the profit-maximizing platform does not subsidize efficiently the "good" side of the market, leading to very little traffic reduction. These results call for a discussion of the regulation of myopic platforms in general, and those of carpooling in particular. |
| Keywords: | Network effect, Information asymmetry, Externality, Working Papers du LAET |
| Date: | 2023–02–14 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-03980205&r=gth |