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on Game Theory |
| By: | Claudia Meroni (Department of Economics (University of Verona)); Carlos Pimienta (School of Economics, The University of New South Wales, Sydney, Australia) |
| Abstract: | In finite games, the graph of the Nash equilibrium correspondence is a semialgebraic set (i.e. it is defined by finitely many polynomial inequal- ities). This fact implies many game theoretical results about the structure of equilibria. We show that many of these results can be readily exported to Poisson games even if the expected utility functions are not polynomials. We do this proving that, in Poisson games, the graph of the Nash equilibrium correspondence is a globaly subanalytic set. Many of the properties of semialgebraic sets follow from a set of axioms that the collection of globaly subanalytic sets also satisfy. Hence, we easily show that every Poisson game has finitely many connected components and that at least one of them contains a stable set of equilibria. By the same reasoning, we also show how generic determinacy results in finite games can be extended to Poisson games. |
| Keywords: | Poisson games, voting, stable sets, o-minimal structures, globaly subanalytic sets. |
| JEL: | C70 C72 |
| Date: | 2015–10 |
| URL: | http://d.repec.org/n?u=RePEc:ver:wpaper:25/2015&r=all |
| By: | UI, Takashi |
| Abstract: | This paper provides a sufficient condition for the existence and uniqueness of a Bayesian Nash equilibrium by regarding it as a solution of a variational inequality. The payoff gradient of a game is defined as a vector whose component is a partial derivative of each player's payoff function with respect to the player's own action. If the Jacobian matrix of the payoff gradient is negative definite for each state, then a Bayesian Nash equilibrium is unique. This result unifies and generalizes the uniqueness of an equilibrium in a complete information game by Rosen (Econometrica 33: 520, 1965) and that in a team by Radner (Ann. Math. Stat. 33: 857, 1962). In a Bayesian game played on a network, the Jacobian matrix of the payoff gradient coincides with the weighted adjacency matrix of the underlying graph. |
| Keywords: | Bayesian game, network game, potential game, team, variational inequality, payoff gradient, strict monotonicity |
| JEL: | C72 D82 |
| Date: | 2015–10 |
| URL: | http://d.repec.org/n?u=RePEc:hit:econdp:2015-08&r=all |
| By: | A.K.S. Chand; Sergio Currarini; Giovanni Ursino (Università Cattolica del Sacro Cuore; Dipartimento di Economia e Finanza, Università Cattolica del Sacro Cuore) |
| Abstract: | We consider a game of information transmission, with one informed decision maker gathering information from one or more informed senders. Private information is (conditionally) correlated across players, and communication is cheap talk. For the one sender case, we show that correlation unambiguously tightens the existence conditions for a truth-telling equilibrium. We then generalize the model to an arbitrary number of senders, and we find that, in this case, the effect of correlation on the incentives to report information truthfully is non monotone, and correlation may discipline senders' equilibrium behavior, making it easier to sustain truth-telling. |
| Keywords: | Cheap Talk, Multiple Senders, Correlation |
| JEL: | C72 D82 D83 |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:ctc:serie1:def024&r=all |
| By: | Iñaki Aldasoro; Domenico Delli Gatti (Università Cattolica del Sacro Cuore; Dipartimento di Economia e Finanza, Università Cattolica del Sacro Cuore); Ester Faia |
| Abstract: | We present a network model of the interbank market in which optimizing risk averse banks lend to each other and invest in non-liquid assets. Market clearing takes place through a tâtonnement process which yields the equilibrium price, while traded quantities are determined by means of a matching algorithm. We compare three alternative matching algorithms: maximum entropy, closest matching and random matching. Contagion occurs through liquidity hoarding, interbank interlinkages and fire sale externalities. The resulting network configurations exhibits a core-periphery structure, dis-assortative behavior and low clustering coefficient. We measure systemic importance by means of network centrality and input-output metrics and the contribution of systemic risk by means of Shapley values. Within this framework we analyze the effects of prudential policies on the stability/efficiency trade-off. Liquidity requirements unequivocally decrease systemic risk but at the cost of lower efficiency (measured by aggregate investment in non-liquid assets); equity requirements tend to reduce risk (hence increase stability) without reducing significantly overall investment. |
| Keywords: | banking networks, centrality metrics, systemic risk |
| JEL: | D85 G21 G28 C63 L14 |
| Date: | 2015–07 |
| URL: | http://d.repec.org/n?u=RePEc:ctc:serie1:def028&r=all |
| By: | Eric Guerci (Université Nice Sophia Antipolis; GREDEG-CNRS); Nobuyuki Hanaki (Université Nice Sophia Antipolis; GREDEG-CNRS; IUF); Naoki Watanabe (University of Tsukuba, Japan) |
| Abstract: | By employing binary committee choice problems, this paper investigates how varying or eliminating feedback about payoffs affects: (1) subjects' learning about the underlying relationship between their nominal voting weights and their expected payoffs in weighted voting games; and (2) the transfer of acquired learning from one committee choice problem to a similar but different problem. In the experiment, subjects choose to join one of two committees (weighted voting games) and obtain a payoff stochastically determined by a voting theory. We found that: (i) subjects learned to choose the committee that generates a higher expected payoff even without feedback about the payoffs they received; and (ii) there was statistically significant evidence of ``meaningful learning'' (transfer of learning) only for the treatment with no payoff-related feedback. This finding calls for re-thinking existing models of learning to incorporate some type of introspection. |
| Keywords: | Learning, voting game, experiment, two-armed bandit problem |
| JEL: | C79 C92 D72 D83 |
| Date: | 2015–10 |
| URL: | http://d.repec.org/n?u=RePEc:gre:wpaper:2015-40&r=all |
| By: | Sebastian Schweighofer-Kodritsch |
| Abstract: | This paper presents an analysis of general time preferences in the canonical Rubinstein (1982) model of bilateral alternating-offers bargaining. I derive a simple sufficient structure for optimal punishments and thereby fully characterize (i) the set of equilibrium outcomes for any given preference profile, and (ii) the set of preference profiles for which equilibrium is unique. When both players have a present bias— empirically, a property of most time preferences regarding consumption, and implied, e.g., by any hyperbolic or quasi-hyperbolic discounting—equilibrium is unique, stationary and efficient. When, instead, one player finds a near-future delay more costly than delay from the present—empirically common for time preferences over money—non stationary equilibria arise that explain inefficiently delayed agreement with gradually increasing offers. |
| Keywords: | alternating offer, time preference, impatience, discounting, dynamic inconsistency, delay, optimal punishment, simple penal codes, non-stationary equilibrium |
| JEL: | C78 D03 D74 |
| Date: | 2015–08 |
| URL: | http://d.repec.org/n?u=RePEc:cep:stitep:/2015/568&r=all |
| By: | Paul Johnson (Department of Economics and Public Policy, University of Alaska Anchorage); Qiujie Zheng (Department of Economics and Public Policy, University of Alaska Anchorage) |
| Abstract: | This paper describes a classroom experiment that demonstrates coordination and competition between traders in a network. Students test theoretical predictions concerning the emergence of equilibrium and the division of surplus between buyers and sellers. The experiment is appropriate for use in teaching intermediate microeconomics, industrial organization, transportation economics and game theory. |
| Keywords: | Experimental Economics, Classroom Experiment, Trading in Networks |
| JEL: | A22 B21 C92 |
| Date: | 2015–10 |
| URL: | http://d.repec.org/n?u=RePEc:ala:wpaper:2015-03&r=all |
| By: | Flavio Pressacco (DIES - DIES - Dept. of Economics and Statistics - University of Udine, Italy); Laura Ziani (DIES - DIES - Dept. of Economics and Statistics - University of Udine, Italy) |
| Abstract: | We define Fibonacci games as the subset of constant sum homogeneous weighted majority games whose increasing sequence of all type weights and the minimal winning quota is a string of consecutive Fibonacci numbers. Exploiting properties of the Fibonacci sequence, we obtain closed form results able to provide a simple and insightful classification and characterization of such games. |
| Keywords: | satellite games., type weight vector, minimal winning coalition, homogeneous representation,Fibonacci numbers, weighted majority games |
| Date: | 2015–09–02 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01196209&r=all |
| By: | Roman M. Sheremeta (Weatherhead School of Management, Case Western Reserve University and Economic Science Institute, Chapman University) |
| Abstract: | Group contests are ubiquitous. Some examples include warfare between countries, competition between political parties, team-incentives within firms, group sports, and rent-seeking. In order to succeed, members of the same group have incentives to cooperate with each other by expending individual efforts. However, since effort is costly, each member also has an incentive to abstain from expending any effort and instead free-ride on the efforts of other members. Contest theory shows that the intensity of competition between groups and the amount of freeriding within groups depend on the group size, sharing rule, group impact function, contest success function, and heterogeneity of players. We review experimental studies testing these theoretical predictions. Almost all studies of behavior in group contests find significant overexpenditure of effort relative to the theory. We discuss potential explanations for such overexpenditure, including the utility of winning, bounded rationality, relative payoff maximization, parochial altruism, and social identity. Despite over-expenditure, most studies find support for the comparative statics predictions of the theory (with the exception of the “group size paradox”). Finally, studies show that there are effective mechanisms that can promote withingroup cooperation and conflict resolution mechanisms that can de-escalate and potentially eliminate between-group conflict. |
| Keywords: | groups, contests, experiments |
| JEL: | C7 C9 D7 H4 J4 K4 L2 M5 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:15-21&r=all |
| By: | Claudia M. Landeo (University of Alberta); Kathryn E. Spier (Harvard Law School and NBER) |
| Abstract: | This paper reports the results of an experiment on incentive contracts for teams. The agents, whose efforts are complementary, are rewarded according to a sharing rule chosen by the principal. Depending on the sharing rule, the agents confront endogenous prisoner's dilemma or stag-hunt environments. Our main findings are as follows. First, we demonstrate that ongoing interaction among team members positively affects the principal's payoff. Greater team cooperation is successfully induced with less generous sharing rules in infinitely-repeated environments. Second, we provide evidence of the positive effects of communication on team cooperation in the absence of ongoing team interaction. Fostering communication among team members does not significantly affect the principal's payoff, suggesting that agents' communication is an imperfect substitute for ongoing team interaction. Third, we show that offering low sharing rules can backfire. The agents are willing to engage in costly punishment (shirking) as retaliation for low offers from the principal. Our findings suggest that offering low sharing rules is perceived by the agents as unkind behavior and hence, triggers negative reciprocity. |
| Keywords: | Moral Hazard in Teams, Prisoner's Dilemma, Stag-Hunt Games, Infinitely-Repeated Games, Communication, Reciprocity, Laboratory Experiments |
| JEL: | C72 C90 D86 K10 L23 |
| Date: | 2015–10 |
| URL: | http://d.repec.org/n?u=RePEc:apc:wpaper:2015-052&r=all |
| By: | Flavio Pressacco (DIES - DIES - Dept. of Economics and Statistics - University of Udine, Italy); Laura Ziani (DIES - DIES - Dept. of Economics and Statistics - University of Udine, Italy) |
| Abstract: | We define Fibonacci games as the subset of constant sum homogeneous weighted majority games whose increasing sequence of all type weights and the minimal winning quota is a string of consecutive Fibonacci numbers. Exploiting properties of the Fibonacci sequence, we obtain closed form results able to provide a simple and insightful classification and characterization of such games. |
| Keywords: | minimal winning coalition, homogeneous representation,Weighted majority games, type weight vector, satellite games, Fibonacci numbers. |
| Date: | 2015–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01214664&r=all |
| By: | George J. Mailath; Andrew Postlewaite; Larry Samuelson |
| Date: | 2015–10–15 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:786969000000001202&r=all |