
on Game Theory 
Issue of 2012‒07‒23
23 papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University 
By:  Stéphane Gonzalez (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  Panthéon Sorbonne); Michel Grabisch (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  Panthéon Sorbonne, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris) 
Abstract:  In cooperative games, the core is one of the most popular solution concept since it ensures coalitional rationality. For nonbalanced 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 kadditive 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 kadditive 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 kadditive 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. 
Date:  2012–04 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs00718358&r=gth 
By:  Philippe Bich (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  Panthéon Sorbonne, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris); Rida Laraki (Ecole Polytechnique  Ecole Polytechnique, IMJ  Institut de Mathématiques de Jussieu  CNRS : UMR7586  Université Paris VI  Pierre et Marie Curie  Université Paris VII  Paris Diderot) 
Abstract:  Several relaxations of Nash equilibrium are shown to exist in strategic games with discontinuous payoff functions. Those relaxations are used to extend and unify several recent results and link Reny's betterreply security condition [Reny, P.J. (1999). On the existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games] to SimonZame's endogenous tiebreaking rules [Simon, L.K. and Zame, W.R. (1990). Discontinuous Games and Endogenous Sharing Rules]. 
Keywords:  Discontinuous games, Nash equilibrium, Reny equilibrium, betterreply security, endogenous sharing rule, quasi equilibrium, finite deviation equilibrium, symmetric games. 
Date:  2012–06 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs00717135&r=gth 
By:  Erik O. Kimbrough (Simon Fraser Unviersity); Alexander Vostroknutov (Maastricht University) 
Abstract:  Rules are thought to persist to the extent that the direct benefits of having them (e.g. reduced transactions costs) exceed the costs of enforcement and of occasional misapplications. We argue that a second crucial role of rules is as screening mechanisms for identifying cooperative types. Thus we underestimate the social value of rules when we consider only their instrumental value in solving a particular problem. We demonstrate experimentally that costly rulefollowing can be used to screen for conditional cooperators. Subjects participate in a rulefollowing task in which they may incur costs to follow an arbitrary written rule in an individual choice setting. Without their knowledge, we sort them into groups according to their willingness to follow the rule. These groups then play repeated public goods or trust games. Rulefollowing groups sustain high public goods contributions over time, but in rulebreaking groups cooperation decays. Rulefollowers also reciprocate more in trust games. However, when individuals are not sorted by type, we observe no differences in the behavior of rulefollowers and rulebreakers. 
Keywords:  experimental economics, rules, social dilemmas, cooperation 
JEL:  C91 C92 D70 D03 
Date:  2012–07 
URL:  http://d.repec.org/n?u=RePEc:sfu:sfudps:dp1215&r=gth 
By:  Teng, Jimmy 
Abstract:  This paper proposes a way to solve two (and multiple) sided incomplete information games which generally generates a unique equilibrium. The approach uses iterative conjectures updated by game theoretic and Bayesian statistical decision theoretic reasoning. Players in the games form conjectures about what other players want to do, starting from first order uninformative conjectures and keep updating with games theoretic and Bayesian statistical decision theoretic reasoning until a convergence of conjectures is achieved. The resulting convergent conjectures and the equilibrium (which is named Bayesian equilibrium by iterative conjectures) they supported form the solution of the game. The paper gives two examples which show that the unique equilibrium generated by this approach is compellingly intuitive and insightful. The paper also solves an example of a three sided incomplete information simultaneous game. 
Keywords:  new equilibrium concept; two and multiple sided incomplete information; iterative conjectures; convergence; Bayesian decision theory; Schelling point 
JEL:  C70 C72 
Date:  2012–03–01 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:40061&r=gth 
By:  Martin Shubik (Cowles Foundation, Yale University) 
Abstract:  These notes are provided to describe many of the problems encountered concerning both structure and behavior in specifying what is meant by the solution to a game of strategy in matrix or strategic form. In the short term in particular, it is often reasonable for the individual to accept as given, both the context in which decisions are being made and the formal structure of the rules of the game. A solution is usually considered as a complete set of equations of motion that when applied to the game at hand selects a final outcome. There are many different theories and conjectures about how games of strategy are, or should be played. Several of them are noted below. They are especially relevant to the experimental gaming facility noted in the companion paper. 
Keywords:  Matrix games, Solution concepts, Experimental gaming 
JEL:  C7 C9 
Date:  2012–07 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:1866&r=gth 
By:  Velu, Chander (University of Cambridge); Iyer, Sriya (University of Cambridge); Gair, Jonathan R. (University of Cambridge) 
Abstract:  Players cooperate in experiments more than game theory would predict. In order to explain this, we introduce the 'returnsbased beliefs' approach: the expected returns of a particular strategy in proportion to the total expected returns of all strategies. Using a decision analytic solution concept, Luce's (1959) probabilistic choice model, and 'hyperpriors' for ambiguity in players' cooperability, our approach explains empirical observations in classic games such as the Prisoner's Dilemma. Testing the closeness of fit of our model on Selten and Chmura (2008) data for completely mixed 2x2 games shows that with loss aversion, returnsbased beliefs explain the data better than other equilibrium concepts. 
Keywords:  subjective probabilities, decision making, cooperation 
JEL:  D01 D03 
Date:  2012–07 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp6711&r=gth 
By:  Siegfried K. Berninghaus; Werner Güth (Max Planck Institute of Economics, Strategic Interaction Group); King King Li 
Abstract:  "Approximate truth" refers to the principle that border cases should be analyzed by solving generic cases and solving border cases as limits of generic ones (Brennan et al., 2008). Our study experimentally explores whether this conceptual principle is also behaviorally appealing. To do so, we focus on perfectness (Selten, 1975) and use his example game with (no) multiplicity of (perfect) equilibria. Distinguishing three uniform perturbation levels, we check for monotonicity (all players react monotonically to the perturbation level) and then explore the behavioral relevance of "approximate truth." 
Keywords:  experimental games, trembling hand perfectness, perturbed strategies 
JEL:  C70 C72 C91 
Date:  2012–07–11 
URL:  http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2012040&r=gth 
By:  Madhav S. Aney (School of Economics, Singapore Management University) 
Abstract:  This paper considers the problem of allocating an object between two players in an environment with one sided asymmetric information when their outside options depend on each other's type, causing the outside option of the uninformed player to be unobservable to her. Consequently efficient mechanisms under budget balance are not always available even when there is no uncertainty about which of the two players values the object more. A simple condition on the outside options turns out to be both necessary and sufficient to guarantee the first best. I also characterise the second best allocation under some conditions and show how it varies with changes in the outside options. I argue that the model applies to an environment where property rights over the object are not well defined and their enforcement is subject to an inefficient default game such as a contest. In such cases type dependent outside options arise naturally as the equilibrium payos from the default game. The model can explain why the best ways of avoiding inefficient default games, such as arbitration as a way of avoiding litigation, typically involve a degree of inefficiency. 
Date:  2012–07 
URL:  http://d.repec.org/n?u=RePEc:siu:wpaper:282012&r=gth 
By:  Eike Kroll (Faculty of Economics and Management, OttovonGuericke University Magdeburg); Ralf Morgenstern (Faculty of Economics and Management, OttovonGuericke University Magdeburg); Thomas Neumann (Faculty of Economics and Management, OttovonGuericke University Magdeburg); Stephan Schosser (Faculty of Economics and Management, OttovonGuericke University Magdeburg); Bodo Vogt (Faculty of Economics and Management, OttovonGuericke University Magdeburg) 
Abstract:  While experimental research on social dilemmas focuses on the distribution of gains, this paper analyzes social preferences in the case of losses. In this experimental study, participants share a loss in a Nash bargaining game. Instead of monetary losses, we use waiting time as an incentive. We assume that participants prefer less to more waiting time. Our experiment consists of four versions of the Nash bargaining game, which vary in a way that allows a comparison of four classical concepts on negotiations (Nash, Equal Loss, Equal Gain, and KalaiSmorodinski), and Inequality Aversion. We find an equal split of waiting time for all parameter variations. Therefore, our experimental evidence shows that Inequality Aversion provides a better prediction than do classical concepts for the outcome of a Nash bargaining game involving losses. Furthermore, participants resort to Inequality Aversion at the cost of overall welfare. 
Keywords:  bargaining, losses, inequality aversion, experimental economics 
JEL:  C7 C9 
Date:  2012–06 
URL:  http://d.repec.org/n?u=RePEc:mag:wpaper:120014&r=gth 
By:  Jun Xiao 
Abstract:  This paper studies a completeinformation bargaining game with one buyer and multiple sellers of di¤erent ?sizes? or bargaining strengths. The bargaining order is determined by the buyer. If the buyer can commit to a bargaining order, there is a unique subgame perfect equilibrium outcome where the buyer bargains in order of increasing size ? from the smallest to the largest. If the buyer cannot commit to a bargaining order and the sellers are su¢ ciently di¤erent, there is also a unique subgame perfect equilibrium outcome again with the order of increasing size. 
Keywords:  multiperson bargaining, bargaining order 
JEL:  C78 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:mlb:wpaper:1150&r=gth 
By:  Fabbri, Marco (Associazione Italiana per la Cultura della Cooperazione e del Non Profit) 
Abstract:  The aim of this work is to show that in a repeated Public Goods Game situation it is possible, through the implementation of a properly specified policy reward, to increase and sustain higher level of contribution with respect to the only "punishment" equilibrium at net zero costs. I investigate theoretically the possibility that implementing a lottery, mechanism in a social dilemma could drive a consistent portion of the game participants’ decision to a different decision choice with respect to Von NeumannMorgenstern Expected Utility Theory prediction. In particular, grounding my expectations on Cumulative Prospect Theory, I anticipate and exploit the players’ overweight of an unlikely event such as the gain deriving from the extraction of a single high prize assigned randomly at the end of all the treatments to one individual among the subgroup of players that choose to contribute at least the prescribed amount to the public good. I present a model that exploiting this regularity in economic decision making and endogenizing the probability of winning the final prize could increase the level of contribution to the public good without additional expenditure. Then I test this theoretical prediction setting up a controlled laboratory experiment. 
Date:  2012–06–26 
URL:  http://d.repec.org/n?u=RePEc:ris:aiccon:2012_109&r=gth 
By:  Oliver Kirchkamp (School of Economics and Business Administration, FriedrichSchillerUniversity Jena); Ulrike Vollstädt (Jena Graduate School "Human Behaviour in Social and Economic Change", University of Jena) 
Abstract:  Although many real bargaining situations involve more than two people, much of the theoretical and experimental research concentrates on the two player situation. We study the simplest possible extension: four people (two twoperson groups) of different patience bargain with each other. Theoretically, only the more patient member of each group should be relevant for the outcome. The less patient members would agree to any outcome and are, hence, irrelevant. We find, however, that the impact of the patient member can be quite small. 
Keywords:  bargaining experiment, heterogeneous group members 
JEL:  C78 D74 
Date:  2012–07–16 
URL:  http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2012043&r=gth 
By:  Bergantiños, Gustavo; VidalPuga, Juan 
Abstract:  We characterize, in minimum cost spanning tree problems, the family of rules satisfying monotonicity over cost and population. We also prove that the set of allocations induced by the family coincides with the irreducible core. 
Keywords:  Cost sharing; minimum cost spanning tree problems; monotonicity; irreducible core 
JEL:  C71 
Date:  2012–07 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:39994&r=gth 
By:  Siegfried K. Berninghaus (Karlsruhe Institute of Technology, Institute for Economic Theory and Statistics); Werner Güth (Max Planck Institute of Economics, Strategic Interaction Group); Stephan Schosser (University of Magdeburg, Chair of Empirical Economics) 
Abstract:  Bounded rationality questions backward induction, which however, does not exclude such reasoning when anticipation is easy. In our stochastic (alternating offer) bargaining experiment, there is a certain firstperiod pie and a known finite deadline. What is uncertain (except for the final period) is whether there is a further period. Whereas backward induction requires information about all later pie sizes and probabilities, forward reasoning is expected to consider only the immediate prospects. Rather than relying only on decision data, we try to assess the cognitive approach such as forward reasoning of backward induction by control of information retrieval. We find that participants who begin with the shortest games before playing possibly longer games, initially resort to backward induction before switching to forwardlooking behavior. 
Keywords:  backward induction, forward reasoning, bargaining 
JEL:  C70 C72 C91 
Date:  2012–07–12 
URL:  http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2012041&r=gth 
By:  Jun Xiao 
Abstract:  This paper studies completeinformation, allpay contests with asymmetric players competing for multiple heterogeneous prizes. In these contests, each player chooses a performance level or score. The first prize is awarded to the player with the highest score,the second,less valuable prize to the player with the second highest score, etc. Players are asymmetric in that they incur di¤erent costs of score. The players are assumed to have ordered marginal costs, and the prize sequence is assumed to be either quadratic or geometric. I show that each such contest has a unique Nash equilibrium and exhibit an algorithm that constructs the equilibrium. I then apply the main result to study: (a) the issue of tracking students in schools, (b) the incentive e¤ects of superstars,and (c)the optimality of winnertakeall contests. 
Keywords:  allpay, contest, asymmetric, heterogeneous 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:mlb:wpaper:1151&r=gth 
By:  Schubert, Manuel; Graf Lambsdorff, Johann 
Abstract:  Psychology has inspired economics to recognize intentions in addition to outcomes as being relevant for utility and behavior. Reciprocal behavior, in particular, has been related to the kindness of chosen actions and how kindness can be derived from the benefits obtained in unchosen alternatives. This study shows that a richer understanding of kindness is required. We carry out ultimatum games with a reduced space of strategies and observe that subjects refrain from negative reciprocity (rejecting proposals) if an unchosen alternative was costly to the proposer. Second, we find proposers to anticipate this behavior. Not only the benefits are relevant for assessments of kindness, the costs of kindness matter as well.  
Keywords:  intentions,reciprocity,fairness 
JEL:  C70 C91 D63 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:zbw:upadvr:v6412&r=gth 
By:  Dai, Darong 
Abstract:  In the paper, we reinvestigate the long run behavior of an adaptive learning process driven by the stochastic replicator dynamics developed by Fudenberg and Harris (1992). It is demonstrated that the Nash equilibrium will be the robust limit of the adaptive learning process as long as it is reachable for the learning dynamics in almost surely finite time. Doob’s martingale theory and Girsanov Theorem play very important roles in confirming the required assertion. 
Keywords:  Stochastic replicator dynamics; Adaptive learning; Nash equilibria; Global convergence; Robustness 
JEL:  C72 C73 
Date:  2012–05–03 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:40040&r=gth 
By:  Engwerda, J.C.; Aarle, B. van; Plasmans, J.E.J.; Weeren, A.J.T.M. (Tilburg University, Center for Economic Research) 
Abstract:  Abstract: As a result of the recent financial crisis and the ensuing economic recession, fiscal deficits have soared in many OECD countries. As a consequence, government debt has been on the rise again after a period of stable or declining government debt. In this paper we analyze debt stabilization in a country that features endogenous risk premia, imposed by financial markets that evaluate the probability of debt default by governments. Endogenous risk premia arise by assuming e.g. simple linear relations between risk premia and the level of debt. As a result the real interest rate on government debt can be written as a constant (measuring the riskfree real interest rate corrected for real output growth) plus an endogenous risk premium that depends on the debt level. We bring such endogenous risk premia into the Tabellini (1986) model [22] and analyze the impact of it. This gives rise to a nonlinear differential game. We solve this game for both a cooperative setting and a noncooperative setting. The noncooperative game is solved under an openloop information structure. In particular we present a bifurcation analysis w.r.t. the risk premium parameter. 
Keywords:  debt stabilization;differential games;nonlinear dynamical systems;economic dynamics. 
JEL:  C7 C62 E6 F4 H6 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:dgr:kubcen:2012056&r=gth 
By:  James Bland, Simon Loertscher 
Abstract:  We consider the canonical directed search framework in which sellers play pure strategies and assume that buyers play strategies that are monotone in prices, can remain inactive and choose to do so whenever their payoff from participating is zero regardless of what the other buyers do. We show that directed search equilibria, which have been the focus of the literature, are the only equilibria that satisfy these assumptions. Directed search equilibria are selected here not because buyers cannot coordinate – no such assumption is made – but because they fail to play strategies that require them to increase the demand for a seller’s good as this good becomes more expensive. 
Keywords:  Directed search, monotone strategies, directed search equilibrium. 
JEL:  C72 D72 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:mlb:wpaper:1147&r=gth 
By:  Alfredo Di Tillio; Nenad Kos; Matthias Messner 
Abstract:  This paper considers the optimal mechanism design problem of an expected revenue maximizing principal who wants to sell a single unit of a good to an agent who is ambiguity averse in the sense of Gilboa and Schmeidler (1989). We show that the optimal static mechanism is an ambiguous mechanism. An ambiguous mechanism specifies a message space and a set of outcome functions. After showing that (a version of) the Revelation Principle holds in our environment, we give an exact characterization of the (smallest) optimal ambiguous mechanism. If the type set is composed of N (finite) types, then the (smallest) optimal ambiguous mechanism contains N  1 outcome functions. We show that the share of the surplus that the designer can extract from the agent increases as the type set becomes larger and the probability of each single type decreases. In the limiting case where the agent’s type is drawn from a nonatomic distribution on an interval, the optimal ambiguous mechanism extracts all the rent from the agent. 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:igi:igierp:446&r=gth 
By:  Jorge M. Streb; Gustavo Torrens 
Abstract:  Under asymmetric information, dishonest sellers lead to market unraveling in the lemons model. An additional cost of dishonesty is that language becomes cheap talk. We develop instead a model where people derive utility from actions (what they say), as well as from outcomes, so talk is costly. We find that the existence of honest agents that mean what they say is not enough to make trade more likely, unless a traceability condition that prevents arbitrage is met. When we introduce a continuum of misrepresentation cost types and qualities, full market unraveling is not possible and babbling equilibria are eliminated. More generally, costly talk is a special kind of signal, a symbolic signal that presupposes linguistic conventions, otherwise truth and falsehood, as well as misrepresentation costs, are undefined. 
Keywords:  asymmetric information, honesty, trust, symbols, signals, costly talk 
JEL:  D8 C7 
Date:  2012–07 
URL:  http://d.repec.org/n?u=RePEc:cem:doctra:492&r=gth 
By:  Claudio Mezzetti & Ludovic Renou 
Abstract:  We study the gains from trade in a model with endogenously variable markups. We show that the procompetitive gains from trade are large if the economy is characterized by (i) extensive misallocation, i.e., large ineciencies associated with markups, and (ii) a weak pattern of crosscountry comparative advantage in individual sectors. We and strong evidence for both of these ingredients using producerlevel data for Taiwanese manufacturing establishments. Parameterizations of the model consistent with this data thus predict large procompetitive gains from trade, much larger than those in standard Ricardian models. In stark contrast to standard Ricardian models, data on changes in trade volume are not sucient for determining the gains from trade. 
Keywords:  Implementation, Maskin monotonicity, pure and mixed Nash equilibrium, 
JEL:  C72 D71 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:mlb:wpaper:1146&r=gth 
By:  Martin Dózsa (Institute of Economic Studies, Faculty of Social Sciences, Charles University, Prague, Czech Republic); Jakub Seidler (Institute of Economic Studies, Faculty of Social Sciences, Charles University, Prague, Czech Republic) 
Abstract:  This article presents structural asset pricing model with stochastic interest rate and default barrier based on the evolution of the firm' Earning Before Interest and Taxes (EBIT). This framework is further enhanced by the game theory analysis which examines the negotiation between shareholders and creditors with respect to the debt of the company and its safety covenants serving as the default trigger. As a result, this complex framework allows toanalyse different optimal capital structures of the company and its default probability dependent on the changes in the riskfree interest rate, which may also represent the current state of the economy. As the numerical computations show this approach is more convenient than the constant default barrier framework used in the currently available literature. 
Keywords:  credit contracts, stochastic default barrier, asset pricing, EBITbased models, structural models 
JEL:  C73 G12 G32 G33 
Date:  2012–06 
URL:  http://d.repec.org/n?u=RePEc:fau:wpaper:wp2012_17&r=gth 