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on Game Theory |
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Issue of 2012‒05‒02
sixteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Hernández, Penélope (ERI-CES. Departamento de Análisis Económico. Facultad de Economía.); Silva-Reus, José A. (Instituto Interuniversitario de Desarrollo Social y Paz) |
| Abstract: | This note provides a way to translate an n-person strategic game to a characteristic cooperative game assuming that the set of players of the cooperative game is the set of pure actions of the strategic game. The Core is characterized through coalitions generated with only one action for each player and the total coalition. We obtain the worth of the total coalition to guarantee the non-emptyness condition. In particular, for a two-player game, this value is equal to the maximal sum of the diagonals. |
| Keywords: | Cooperative games; Core |
| JEL: | C71 C72 |
| Date: | 2012–04–24 |
| URL: | http://d.repec.org/n?u=RePEc:ris:qmetal:2012_009&r=gth |
| By: | Peter Duersch; Joerg Oechssler; Burkhard Schipper (Department of Economics, University of California Davis) |
| Abstract: | We show that for many classes of symmetric two-player games, the simple decision rule ``imitate-if-better'' can hardly be beaten by any strategy. We provide necessary and sufficient conditions for imitation to be unbeatable in the sense that there is no strategy that can exploit imitation as a money pump. In particular, imitation is subject to a money pump if and only if the relative payoff function of the game is of the rock-scissors-paper variety. We also show that a sufficient condition for imitation not being subject to a money pump is that the relative payoff game is a generalized ordinal potential game or a quasiconcave game. Our results apply to many interesting examples of symmetric games including 2 x 2 games, Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games. |
| Keywords: | Imitate-the-best, learning, symmetric games, relative payoffs, zero-sum games, rock-paper-scissors, finite population ESS, generalized ordinal potential games, quasiconcave games |
| JEL: | C72 C73 D43 |
| Date: | 2012–04–17 |
| URL: | http://d.repec.org/n?u=RePEc:cda:wpaper:12-5&r=gth |
| By: | Thomas W.L. Norman |
| Abstract: | If players learn to play an infinitely repeated game using Bayesian learning, it is known that their strategies eventually approximate Nash equilibria of the repeated game under an absolute-continuity assumption on their prior beliefs. We suppose here that Bayesian learners do not start with such a “grain of truth”, but with arbitrarily low probability they revise beliefs that are performing badly. We show that this process converges in probability to a Nash equilibrium of the repeated game. |
| Keywords: | Repeated games, Nash equilibrium, Rational learning, Bayesian learning, Absolute continuity |
| JEL: | C73 D83 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:602&r=gth |
| By: | Stéphane Gonzalez (Centre d'Economie de la Sorbonne - Paris School of Economics); Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics) |
| Abstract: | In cooperative games, the core is one of the most popular solution concept since it ensures coalitional rationality. For non-balanced games however, the core is empty, and other solution concepts have to be found. We propose the use of general solutions, that is, to distribute the total worth of the game among groups rather than among individuals. In particular, the k-additive core proposed by Grabisch and Miranda is a general solution preserving coalitional rationality which distributes among coalitions of size at most k, and is never ampty for k ? 2. The extended core of Bejan and Gomez can also be viewed as a general solution, since it implies to give an amount to the grand coalition. The k-additive core being an unbounded set and therefore difficult to use in practice, we propose a subset of it called the minimal bargaining set. The idea is to select elements of the k-additive core minimizing the total amount given to coalitions of size greater than 1. Thus the minimum bargaining set naturally reduces to the core for balanced games. We study this set, giving properties and axiomatizations, as well as its relation to the extended core of Bejan and Gomez. We introduce also the notion of unstable coalition, and show how to find them using the minimum bargaining set. Lastly, we give a method of computing the minimum bargaining set. |
| Keywords: | Cooperative game, core, balancedness, general solution. |
| JEL: | C71 |
| Date: | 2012–04 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:12022&r=gth |
| By: | Marion Oury (THEMA, Universite de Cergy-Pontoise) |
| Abstract: | This paper examines many-player many-action global games with multidimensional state parameters. It establishes that the notion of noise-independent selection introduced by Frankel, Morris and Pauzner (Journal of Economic Theory 108 (2003) 1- 44) for onedimensional global games is robust when the setting is extended to the one proposed by Carlsson and Van Damme (Econometrica, 61, 989-1018). More precisely, our main result states that if an action prole of some complete information game is noise-independently selected in some one-dimensional global game, then it is also noise-independently selected in all multidimensional global games. |
| Keywords: | equilibrium selection, global games, strategic complementarities, robustness. |
| JEL: | C72 D82 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:ema:worpap:2012-28&r=gth |
| By: | A.W. Beggs |
| Abstract: | This paper studies uniqueness of equilibrium in symmetric 2 x 2 bayesian games. It shows that if signals are highly but not perfectly dependent then players play their risk-dominant actions for all but a vanishing set of signal realizations. In contrast to the global games literature, noise is not assumed to be additive. Dependence is modeled using the theory of copulas. |
| Keywords: | Bayesian games, Global games, Uniqueness, Copulas, Risk dominance |
| JEL: | C72 D82 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:603&r=gth |
| By: | Klaus Kultti; Hannu Salonen; Hannu Vartiainen |
| Abstract: | In this paper we study the number of pure strategy Nash equilibria in large finite n-player games. A distinguishing feature of our study is that we allow general - potentially multivalued - best reply correspondences. Given the number K of pure strategies to each player, we assign to each player a distribution over the number of his pure best replies against each strategy profile of his opponents. If the means of these distributions have a limit (mu)i for each player i as the number K of pure strategies goes to infinity, then the limit number of pure equilibria is Poisson distributed with a mean equal to the product of the limit means (mu)i. In the special case when all best reply mappings are equally likely, the probability of at least one pure Nash equilibrium approaches one and the expected number of pure Nash equilibria goes to infinity. |
| Keywords: | random games, pure Nash equilibria, n players |
| JEL: | C62 C72 |
| Date: | 2011–12 |
| URL: | http://d.repec.org/n?u=RePEc:tkk:dpaper:dp71&r=gth |
| By: | Borkotokey, Surajit; Sarangi, Sudipta |
| Abstract: | We propose an allocation rule that takes into account the importance of players and their links and characterizes it for a fixed network. Unlike previous rules, our characterization does not require component additivity. Next, we extend it to flexible networks a la Jackson (2005). Finally, we provide a comparison with other fixed (network Myerson and Position value) and flexible network (player and link based) allocation rules through a number of examples. |
| Keywords: | Network games; Allocation rules; Cooperative games |
| JEL: | C71 D85 A14 |
| Date: | 2011–12–02 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:38340&r=gth |
| By: | Julian C. Jamison |
| Abstract: | Intuitively, we expect that players who are allowed to engage in costless communication before playing a game would be foolish to agree on an inefficient equilibrium. At the same time, however, such preplay communication has been suggested as a rationale for expecting Nash equilibrium in general. This paper presents a plausible formal model of cheap talk that distinguishes and resolves these possibilities. Players are assumed to have an unlimited opportunity to send messages before playing an arbitrary game. Using an extension of fictitious play beliefs, minimal assumptions are made concerning which messages about future actions are credible and hence contribute to final beliefs. In this environment it is shown that meaningful communication among players leads to a Nash equilibrium (NE) of the action game. Within the set of NE, efficiency then turns out to be a consequence of imposing optimality on the cheap talk portion of the extended game. This finding contrasts with previous "babbling" results. |
| Keywords: | Game theory ; Stochastic analysis |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedbwp:12-3&r=gth |
| By: | Paula Jaramillo; Çagtay Kayi; Flip Klijn |
| Abstract: | We study a particular restitution problem where there is an indivisible good (land or property) over which two agents have rights: the dispossessed agent and the owner. A third party, possibly the government, seeks to resolve the situation by assigning rights to one and compensate the other. There is also a maximum amount of money available for the compensation. We characterize a family of asymmetrically fair rules that are immune to strategic behavior, guarantee minimal welfare levels for the agents, and satisfy the budget constraint. |
| Date: | 2012–03–13 |
| URL: | http://d.repec.org/n?u=RePEc:col:000089:009425&r=gth |
| By: | Hannu Salonen |
| Abstract: | We study information aggregation problems where to a set of measures a single measure of the same dimension is associated. The collection of measures could represent the beliefs of agents about the state of the world, and the aggregate would then represent the beliefs of the population. Individual measures could also represent the connectedness of agents in a social network, and the aggregate would reflect the importance of each individual. We characterize the aggregation rule that resembles the Nash welfare function. In the special case of probability aggregation problems, this rule is the only one that satisfies Bayesian updating and some well-known axioms discussed in the literature. |
| Keywords: | belief aggregation, belief updating, Nash welfare function |
| JEL: | C71 D63 D74 |
| Date: | 2012–03 |
| URL: | http://d.repec.org/n?u=RePEc:tkk:dpaper:dp73&r=gth |
| By: | Gill, David; Prowse, Victoria |
| Abstract: | In this paper we investigate how cognitive ability influences behavior, success and the evolution of play towards Nash equilibrium in repeated strategic interactions. We study behavior in a p-beauty contest experiment and find striking differences according to cognitive ability: more cognitively able subjects choose numbers closer to equilibrium, converge more frequently to equilibrium play and earn more even as behavior approaches the equilibrium prediction. To understand better how subjects with different cognitive abilities learn differently, we estimate a structural model of learning based on level-k reasoning. We find a systematic positive relationship between cognitive ability and levels; furthermore, the average level of more cognitively able subjects responds positively to the cognitive ability of their opponents, while the average level of less cognitively able subjects does not respond at all. Our results suggest that, in strategic environments, higher cognitive ability translates into better analytic reasoning and a better ‘theory of mind’ |
| Keywords: | Cognitive ability; Bounded rationality; Learning; Convergence; Level-k; Nonequilibrium behavior; Beauty contest; Repeated games; Structural modeling; Theory of mind; Intelligence; Raven test |
| JEL: | D83 C73 C91 |
| Date: | 2012–04–23 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:38317&r=gth |
| By: | Hannu Salonen |
| Abstract: | Pure strategy Markov perfect equilibria (MPE) in dynamic cake sharing problems are analyzed. Each player chooses under perfect information how much to eat from the current cake and how much to leave to the next period. The left over cake grows according to a given growth function. With linear utilities and strictly concave increasing growth function the only symmetric equilibrium with continuous strategies is the trivial equilibrium in which a player eats the whole cake whenever it is his turn to move. This is quite different than in the corresponding single person decision problem (or at a social optimum) where the cake grows from small initial values towards the steady state. A non-trivial equilibrium with a positive steady state exist in the game. In such an equilibrium strategies cannot be continuous. When utilities are concave and the growth function is linear, a nontrivial MPE with a positive steady state may not exist. |
| Keywords: | common pool resources, dynamic cake sharing, Markov perfect equilibrium |
| JEL: | C72 C73 D92 |
| Date: | 2012–03 |
| URL: | http://d.repec.org/n?u=RePEc:tkk:dpaper:dp72&r=gth |
| By: | Damien Besancenot (CEPN - Centre d'Economie de l'Université Paris Nord - Université Paris XIII - Paris Nord - CNRS : UMR7234); Delphine Dubart (ESSEC Business School - ESSEC Business School); Radu Vranceanu (Economics Department - ESSEC Business School) |
| Abstract: | Humans can lie strategically in order to leverage on their negotiation power. For instance, governments can claim that a "scapegoat" third party is responsible for reforms that impose higher costs on citizens, in order to make the pill sweeter. This paper analyzes such communication strategy within a variant of the ultimatum game. The first player gets an endowment, and the second player can impose a tax on it. The former can reject the allocation submitted by the tax-setter. A third party is then allowed to levy its own tax, and its intake is private information to the tax-setter. In a frameless experiment, 65% of the subjects in the tax-setter role overstate the tax levied by the third party in order to manipulate taxpayer's expectations and submit less advantageous offers; on average, for every additional currency unit of lie, measured by the gap between the claimed and the actual tax, they would reduce their offer by 0.43 currency units. |
| Keywords: | Ultimatum game ; Taxation ; Lies ; Deception ; Asymmetric information |
| Date: | 2012–03–16 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-00690409&r=gth |
| By: | Morone, Andrea; Morone, Piergiuseppe |
| Abstract: | This paper provides an experimental test of the traveller’s dilemma using individual and group data. Our investigation aims to address three fundamental research questions, which can be summarised as follows: (i) claims are affected by the size of the penalty/reward; (ii) individual decisions differ significantly from group decisions; (iii) individual claims are affected by the induction of a focal point a là Schelling. Experimental findings reported in this paper provide answers to each of these questions showing that: (i) although the size of the penalty/reward did not affect subject choices in the first-period, it played a key role in determining subjects’ behaviour in the repeated game; (ii) overall, groups behave more rationally, in the sense that they were always closer to the Nash equilibrium; (iii) the reference point did not encourage coordination around the Pareto optimal choice. |
| Keywords: | traveller’s dilemma; focal point; individual and group decision |
| JEL: | D70 C92 C91 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:38199&r=gth |
| By: | Mallesh Pai; Rakesh Vohra |
| Abstract: | Government procurement and allocation programs often use subsidies and set-asides favoring small businesses and other target groups to address fairness concerns. These concerns are in addition to standard objectives such as efficiency and revenue. We study the design of the optimal mechanism for a seller concerned with efficiency, subject to a constraint to favor a target group. In our model, buyers' private values are determined by costly pre-auction investment. If the constraint is distributional, i.e. to guarantee that the target group wins `sufficiently often', then the constrained efficient mechanism is a flat subsidy. This is consistent with findings in the empirical literature. In contrast, if the constraint is to ensure a certain investment level by the target group, the optimal mechanism is a type dependent subsidy. In this case a set aside may be better than a flat or percentage subsidy. |
| Date: | 2012–04–08 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1548&r=gth |