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on Game Theory |
| By: | Christian Ewerhart; Kremena Valkanova |
| Abstract: | This paper studies fictitious play in networks of noncooperative two-player games. We show that continuous-time fictitious play converges to Nash equilibrium provided that the overall game is zero-sum. Moreover, the rate of convergence is 1/T , regardless of the size of the network. In contrast, arbitrary n-player zero-sum games do not possess the fictitious-play property. As an extension, we consider networks in which each bilateral game is strategically zero-sum, a weighted potential game, or a two-by-two game. In those cases, convergence requires either a condition on bilateral payoffs or that the underlying network structure is acyclic. The results are shown to hold also for the discrete-time variant of fictitious play, which entails a generalization of Robinson's theorem to arbitrary zero-sum networks. Applications include security games, conflict networks, and decentralized wireless channel selection. |
| Keywords: | Fictitious play, networks, zero-sum games, conflicts, potential games, Miyasawa's theorem, Robinson's theorem |
| JEL: | C72 D83 D85 |
| Date: | 2016–12 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:239&r=gth |
| By: | Diss, Mostapha; Doghmi, Ahmed; Tlidi, Abdelmonaim |
| Abstract: | In this paper we establish the link between strategy-proofness and unanimity in a domain of private good economies with single-peaked preferences. We introduce a new condition and we prove that if this new property together with the requirement of citizen sovereignty are held, a social choice function satisfies strategy-proofness if and only if it is unanimous. As an implication, we show that strategy-proofness and Maskin monotonicity become equivalent. We also give applications to implementation literature: We provide a full characterization for standard Nash implementation and partially honest Nash implementation and we determine a certain equivalence among these theories. |
| Keywords: | Strategy-proofness; Unanimity; Maskin monotonicity, Private goods economies; Single-peaked preferences. |
| JEL: | C7 C72 D7 D71 |
| Date: | 2015–11–06 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:75469&r=gth |
| By: | Pierre Bernhard (Université Côte d’Azur, INRIA); Marc Deschamps (Université de Bourgogne Franche-Comté, CRESE) |
| Abstract: | Cournot model of oligopoly appears as a central model of strategic interaction between competing firms both from a theoretical and applied perspective (e.g antitrust). As such it is an essential tool in the economics toolbox and always a stimulus. Although there is a huge and deep literature on it and as far as we know, we think that there is a ”mouse hole” wich has not already been studied: Cournot oligopoly with randomly arriving producers. In a companion paper [Bernhard and Deschamps, 2016b] we have proposed a rather general model of a discrete dynamic decision process where producers arrive as a Bernoulli random process and we have given some examples relating to oligopoly theory (Cournot, Stackelberg, cartel). In this paper we study Cournot oligopoly with random entry in discrete (Bernoulli) and continuous (Poisson) time, whether time horizon is finite or infinite. Moreover we consider here constant and variable probability of entry or density of arrivals. In this framework, we are able to provide algorithmes answering four classical questions: 1/ what is the expected profit for a firm inside the Cournot oligopoly at the beginning of the game?, 2/ How do individual quantities evolve?, 3/ How do market quantities evolve?, and 4/ How does market price evolve? |
| Keywords: | Cournot market structure, Bernoulli process of entry, Poisson density of arrivals, Dynamic Programming. |
| JEL: | C72 C61 L13 |
| Date: | 2016–11 |
| URL: | http://d.repec.org/n?u=RePEc:crb:wpaper:2016-14&r=gth |
| By: | David Martimort (Paris School of Economics-EHESS); Aggey Semenov (Department of Economics, University of Ottawa); Lars Stole (University of Chicago, Booth School of Business) |
| Abstract: | We characterize the complete set of equilibrium allocations to intrinsic common agency screening games as the set of solutions to self-generating optimization programs. This analysis is performed both for continuous and discrete two-type models. These programs, in turn, can be thought of as maximization problems faced by a fictional surrogate principal with a simple set of incentive constraints that embed the non-cooperative behavior of principals in the underlying game. For the case of continuous types, we provide a complete characterization of equilibrium outcomes for regular environments by relying on techniques developed elsewhere for aggregate games and mechanism design problems with delegation. Those equilibria may be non-differentiable and/or exhibit discontinuities. Among those allocations, we stress the role the maximal equilibrium exhibits a n-fold distortion due to the principals' non-cooperative behavior. It is the unique equilibrium which is implemented by a tariff satisfying a biconjugacy requirement inherited from duality in convex analysis. This maximal equilibrium may not be the most preferred equilibrium allocation from the principals' point of view. We perform a similar analysis in the case of a discrete two-type model. We select within a large set of equilibria by imposing the same requirement of biconjugacy on equilibrium tariffs. Those outcomes are limits of equilibria exhibiting much bunching in nearby continuous type models which fail to be regular and require the use of ironing procedures. |
| Keywords: | Intrinsic common agency, aggregate games, mechanism design with delegation, duality, ironing procedures |
| JEL: | D82 D86 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:ott:wpaper:1618e&r=gth |
| By: | Ulrich Faigle (Universität zu Köln - Mathematisches Institut); Michel Grabisch (PSE - Paris School of Economics, CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | We study linear properties of TU-games, revisiting well-known issues like interaction transforms, the inverse Shapley value problem and potentials. We embed TU-games into the model of cooperation systems and influence patterns, which allows us to introduce linear operators on games in a natural way. We focus on transforms, which are linear invertible maps, relate them to bases and investigate many examples (Möbius transform, interaction transform, Walsh transform and Fourier analysis etc.). In particular, we present a simple solution to the inverse problem in its general form: Given a linear value Φ and a game v, find all games v ′ such that Φ(v) = Φ(v ′). Generalizing Hart and Mas-Colell's concept of a potential, we introduce general potentials and show that every linear value is induced by an appropriate potential . |
| Keywords: | Cooperation system, cooperative game, basis, Fourier analysis,inverse problem, potential, transform |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:hal-01404509&r=gth |
| By: | Carlo Beretta |
| Abstract: | Starting with a prisoner’s dilemma, a simple taxonomy of the possible characteristics of a game is introduced. This forms the basis for discussing repeated interactions and the emergence of personalised rules used in durable relationships. When by their nature, interactions are sporadic, much of the same results can be obtained by the use of social rules. Finally, the use of formal contracts, typically incomplete, and a third party to solve conflicts is outlined. The Appendix contains a summary introduction to the problem of incompleteness of norm systems |
| JEL: | A1 C7 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:dis:wpaper:dis1502&r=gth |
| By: | Carlo Beretta |
| Abstract: | Starting with a prisoner’s dilemma, a simple taxonomy of the possible characteristics of a game is introduced. This forms the basis for discussing repeated interactions and the emergence of personalised rules used in durable relationships. When by their nature, interactions are sporadic, much of the same results can be obtained by the use of social rules. Finally, the use of formal contracts, typically incomplete, and a third party to solve conflicts is outlined. The Appendix contains a summary introduction to the problem of incompleteness of norm systems |
| JEL: | A1 C7 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:dis:wpaper:dis1501&r=gth |
| By: | Dominik Rothenhaüsler (Seminar for Statistics, ETH Zurich); Nikolaus Schweizer (Department of Econometrics and OR, Tilburg University); Nora Szech (Karlsruher Institut für Technologie) |
| Abstract: | This paper analyzes how moral costs affect individual support of morally difficult group decisions. We study a threshold public good game with moral costs. Motivated by recent empirical findings, we assume that these costs are heterogeneous and consist of three parts. The first one is a standard cost term. The second, shared guilt, decreases in the number of supporters. The third hinges on the notion of being pivotal. We analyze equilibrium predictions, isolate the causal effects of guilt sharing, and compare results to standard utilitarian and nonconsequentialist approaches. As interventions, we study information release, feedback, and fostering individual moral standards. |
| Keywords: | moral decision making, committee decisions, diffusion of responsibility, Shared guilt, being pivotal, division of labor, institutions and morals |
| JEL: | D02 D03 D23 D63 D82 |
| Date: | 2016–11 |
| URL: | http://d.repec.org/n?u=RePEc:hka:wpaper:2016-026&r=gth |
| By: | Drugov, Mikhail; Ryvkin, Dmitry |
| Abstract: | In a biased contest, one of the players has an advantage in the winner determination process. We characterize a novel class of biased contest success functions pertaining to such contests and provide necessary and sufficient conditions for zero bias to be a critical point of arbitrary objectives satisfying certain symmetry restrictions. We, however, challenge the common wisdom that unbiased contests are always optimal when contestants are symmetric ex ante or even ex post. We show that contests with arbitrary favorites, i.e., biased contests of symmetric players, can be optimal in terms of various objectives such as expected aggregate effort, the probability to reveal the stronger player as the winner or expected effort of the winner. |
| Keywords: | Biased contest; Biased contest success function; Aggregate effort; Predictive power; Winner's effort |
| JEL: | C72 D63 D72 J71 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:75378&r=gth |
| By: | Cary Deck (University of Arkansas and Economic Science Institute, Chapman University and University of Alaska-Anchorage); Charles J. Thomas (Chapman University and Clemson University) |
| Abstract: | We conduct unstructured negotiations in a laboratory experiment designed to empirically assess the predictive power of three approaches to modeling the multilateral negotiations observed in diverse strategic settings. For concreteness we consider two sellers negotiating with a buyer who wants to make only one trade, with the modeling approaches distinguished by whether the buyer negotiates with the sellers sequentially, simultaneously, or in a “take-it-or-leave-it” fashion. Our experiment features two scenarios within which the three approaches have observationally distinct predictions: a differentiated scenario with one highsurplus and one low-surplus seller, and a homogeneous scenario with identical high-surplus sellers. In both scenarios the buyer tends to trade with a high-surplus seller at terms indistinguishable from those in bilateral negotiations with a high-surplus seller, meaning that introducing a competing seller does not affect the observed terms of trade. Our findings match the predictions from the sequential approach, supporting its use in modeling multilateral negotiations. |
| Keywords: | Negotiations & Bargaining, Laboratory Experiments, Procurement, Mergers & Acquisitions, Personnel Economics, Investment |
| JEL: | C7 C9 D4 L1 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:16-29&r=gth |
| By: | Jeffrey Penney (Pontificia Universidad Javeriana); Erin Tolley (University of Toronto); Elizabeth Goodyear-Grant (Queen's University) |
| Abstract: | We analyze the results of a large-scale experiment wherein subjects participate in a hypothetical primary election and must choose between two fictional candidates who vary by sex and race. We find evidence of affinities along these dimensions in voting behaviour. A number of phenomena regarding these affinities and their interactions are detailed and explored. We find that they compete with each other on the basis of race and gender. Neuroeconomic metrics suggest that people who vote for own race candidates tend to rely more on heuristics than those who do not. |
| Keywords: | Gender, Prejudice, Race, Voting |
| JEL: | D72 C90 J15 J16 |
| Date: | 2016–10 |
| URL: | http://d.repec.org/n?u=RePEc:qed:wpaper:1370&r=gth |
| By: | Dietrich, Franz |
| Abstract: | A group is often construed as a single agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated contribution “Groupthink”, Russell et al. (2015) apply the Bayesian paradigm to groups by requiring group credences to undergo a Bayesian revision whenever new information is learnt, i.e., whenever the individual credences undergo a Bayesian revision based on this information. Bayesians should often strengthen this requirement by extending it to 'non-public' or even 'private' information (learnt by 'not all' or 'just one' individual), or to non-representable information (not corresponding to an event in the algebra on which credences are held). I propose a taxonomy of six kinds of 'group Bayesianism', which differ in the type of information for which Bayesian revision of group credences is required: public representable information, private representable information, public non-representable information, and so on. Six corresponding theorems establish exactly how individual credences must (not) be aggregated such that the resulting group credences obey group Bayesianism of any given type, respectively. Aggregating individual credences through averaging is never permitted. One of the theorems – the one concerned with public representable information – is essentially Russell et al.'s central result (with minor corrections). |
| Keywords: | probabilistic opinion pooling, Bayesian groups, geometric pooling, public information, private information, characterization theorems |
| JEL: | D7 D8 |
| Date: | 2016–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:75363&r=gth |