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on Game Theory |
| By: | Kets, W.; Voorneveld, M. (Tilburg University, Center for Economic Research) |
| Abstract: | The minority game is a simple congestion game in which the players? main goal is to choose among two options the one that is adopted by the smallest number of players. We characterize the set of Nash equilibria and the limiting behavior of several well-known learning processes in the minority game with an arbitrary odd number of players. Interestingly, different learning processes provide considerably different predictions. |
| Keywords: | Learning;congestion games;replicator dynamic;perturbed best response dynamics;quantal response equilibria;best-reply learning |
| JEL: | C72 D83 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200761&r=gth |
| By: | Francesco Ciardiello |
| Abstract: | To give sucient conditions for Nash Equilibrium existence in a continuous game is a central problem in Game Theory. In this paper, we present two games in which we show how the continuity and quasi-concavity hypotheses are unconnected one to each other. Then, we relax the quasiconcavity assumption by exploiting the multiconnected convexity's concept (Mechaiekh & Others, 1998) in spaces without any linear structure. These results will be applied to two non-zero-sum games lacking the classical assumptions and more recent improvements (Ziad, 1997), (Abalo & Kostreva, 2004). As a minor result, some counterexamples about relationship between some continuity conditions due to Lignola (1997), Reny (1999) and Simon (1995) for Nash equilibria existence are obtained. |
| Keywords: | Nash Equilibria Existence; Fixed Point Theorem; Generalized Convexity; 2 Person Game; 3 Person Game; Symmetric Game; Generalized Continuity. |
| JEL: | C72 C62 |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:ufg:qdsems:15-2007&r=gth |
| By: | Voorneveld, M. (Tilburg University, Center for Economic Research) |
| Abstract: | In classical game theory, players have finitely many actions and evaluate outcomes of mixed strategies using a von Neumann-Morgenstern utility function. Allowing a larger, but countable, player set introduces a host of phenomena that are impossible in finite games. Firstly, in coordination games, all players have the same preferences: switching to a weakly dominant action makes everyone at least as well off as before. Nevertheless, there are coordina- tion games where the best outcome occurs if everyone chooses a weakly dominated action, while the worst outcome occurs if everyone chooses the weakly dominant action. Secondly, the location of payoff-dominant equilibria behaves capriciously: two coordination games that look so much alike that even the consequences of unilateral deviations are the same may nevertheless have disjoint sets of payoff-dominant equilibria. Thirdly, a large class of games has no (pure or mixed) Nash equilibria. Following the proverb \the grass is always greener on the other side of the hedge", greener-grass games model constant discontent: in one part of the strategy space, players would rather switch to its complement. Once there, they'd rather switch back. |
| Keywords: | coordination games;dominant strategies;payoff-dominance;nonexistence of equi- librium;tail events. |
| JEL: | C72 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200762&r=gth |
| By: | Kin Chung Lo (Department of Economics, York University) |
| Abstract: | Nash equilibrium presumes that players have expected utility preferences, and therefore the beliefs of each player are represented by a probability measure. Motivated by Ellsberg-type behavior, which contradicts the probabilistic representation of beliefs, we generalize Nash equilibrium in n-player strategic games to allow for preferences conforming to the maxmin expected utility model of Gilboa and Schmeidler [Journal of Mathematical Economics, 18 (1989), 141–153]. With no strings attached, our equilibrium concept can be characterized by the suitably modified epistemic conditions for Nash equilibrium. |
| Keywords: | Agreeing to disagree, Correlated equilibrium, Epistemic conditions, Knightian uncertainty, Multiple priors, Nash equilibrium |
| JEL: | C72 D81 |
| Date: | 2007–09 |
| URL: | http://d.repec.org/n?u=RePEc:yca:wpaper:2007_5&r=gth |
| By: | Kleppe, J.; Reijnierse, J.H. (Tilburg University, Center for Economic Research) |
| Abstract: | This paper analyzes congestion effects on network situations from a cooperative game theoretic perspective. In network situations players have to connect themselves to a source. Since we consider publicly available networks any group of players is allowed to use the entire network to establish their connection. We deal with the problem of finding an optimal network, the main focus of this paper is however to discuss the arising cost allocation problem. For this we introduce two different transferable utility cost games. For concave cost functions we use the direct cost game, where coalition costs are based on what a coalition can do in absence of other players. This paper however mainly discusses network situations with convex cost functions, which are analyzed by the use of the marginal cost game. In this game the cost of a coalition is defined as the additional cost it induces when it joins the complementary group of players. We prove that this game is concave. Furthermore, we define a cost allocation by means of three egalitarian principles, and show that this allocation is an element of the core of the marginal cost game. These results are extended to a class of continuous network situations and associated games. |
| Keywords: | Congestion;network situations;cooperative games;public. |
| JEL: | C61 C71 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200758&r=gth |
| By: | Alessandra Sgobbi (Fondazione Eni Enrico Mattei); Carlo Carraro (University of Venice, Fondazione Eni Enrico Mattei and EuroMediterranean Center on Climate Change) |
| Abstract: | The relevance of bargaining to everyday life can easily be ascertained, yet the study of any bargaining process is extremely hard, involving a multiplicity of questions and complex issues. The objective of this paper is to provide new insights on some dimensions of the bargaining process – asymmetries and uncertainties in particular – by using a non-cooperative game theory approach. We develop a computational model which simulates the process of negotiation among more than two players, who bargain over the sharing of more than one pie. Through numerically simulating several multiple issues negotiation games among multiple players, we identify the main features of players’ optimal strategies and equilibrium agreements. As in most economic situations, uncertainty crucially affects also bargaining processes. Therefore, in our analysis, we introduce uncertainty over the size of the pies to be shared and assess the impacts on players’ strategic behaviour. Our results confirm that uncertainty crucially affects players’ behaviour and modifies the likelihood of a self-enforcing agreement to emerge. The model proposed here can have several applications, in particular in the field of natural resource management, where conflicts over how to share a resource of a finite size are increasing. |
| Keywords: | Bargaining, Non-Cooperative Game Theory, Simulation Models, Uncertainty |
| JEL: | C61 C71 C78 |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2007.81&r=gth |
| By: | Juan D Carrillo; Thomas R Palfrey |
| Date: | 2007–09–03 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:122247000000001463&r=gth |
| By: | Vincent Anesi (University of Nottingham) |
| Abstract: | This paper introduces information aggregation into the standard spatial committee game. We assume that committee members must agree on a decision rule to aggregate their private information on a policy-relevant state of the world. We derive sucient conditions for the ex ante incentive compatible core to be nonempty, and provide some characterization results for incentive compatible core decision rules, called "durable decision rules". In particular, core points of the underlying complete-information game are shown to be constant, durable decision rules of the game with incomplete information if they satisfy some robustness property. Moreover, we show that durable decision rules exist whenever information is Pareto-improving relative to the core of the underlying complete-information game, provided that voters' private signals are weakly informative. |
| Keywords: | Core existence, Incentive compatibility, Information aggregation, Committee |
| JEL: | C71 D71 D78 D82 |
| Date: | 2007–08 |
| URL: | http://d.repec.org/n?u=RePEc:cdx:dpaper:2007-03&r=gth |
| By: | Eduardo Faingold; Yuri Sannikov |
| Date: | 2007–09–03 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:122247000000001487&r=gth |
| By: | Juergen Huber; Martin Shubik; Shyam Sunder |
| Date: | 2007–09–03 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:122247000000001480&r=gth |
| By: | Paul Milgrom |
| Date: | 2007–09–03 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:122247000000001454&r=gth |
| By: | Francesco Ciardiello |
| Abstract: | This paper attempts to underline how the Diagonal Transfer Continuity hypothesis (Baye, Tian and Zhou, 1993) and Better-Reply Security (Reny, 1999) are unconnected between themselves as sucient conditions for stating the existence of Nash equilibria. Besides, various examples and counterexamples regarding Nash equilibria existence Theorem (Baye, Tian and Zhou, 1993) and extensions of maximum existence results for bifunctions established for a function of one variable (Baye and and Zhou,1995). We present, also, a sucient conditions for Diagonal Transfer Continuity. Moreover, an example of quasi-concave game having multiple Nash equilibria, in which the aforesaid hypotheses and other improvements (Lignola, 1997) fall, is presented. |
| Keywords: | Nash Equilibria Existence; Generalized Convexity; 2 Person Game; Generalized Continuity; Diagonal Transfer Quasi Concavity; Diagonal Transfer Continuity. |
| JEL: | C72 C62 |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:ufg:qdsems:16-2007&r=gth |
| By: | Ozen, U.; Slikker, M.; Norde, H.W. (Tilburg University, Center for Economic Research) |
| Abstract: | In this paper, we introduce a general framework for situations with decision making under uncertainty and cooperation possibilities. This framework is based upon a two stage stochastic programming approach. We show that under relatively mild assumptions the cooperative games associated with these situations are totally balanced and, hence, have non-empty cores. Finally, we consider several example situations, which can be studied using this general framework. |
| Keywords: | Two-stage stochastic programming; cooperative game theory; core. |
| JEL: | C71 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200757&r=gth |
| By: | Nicolás Figueroa; Vasiliki Skreta |
| Abstract: | This paper studies revenue maximizing auctions when buyers’ outside options depend on their private information. The set-up is very general and encompasses a large number of potential applications. The main novel message of our analysis is that with type-dependent non-participation payoffs, the revenue maximizing assignment of objects can crucially depend on the outside options that buyers face. Outside options can therefore affect the degree of efficiency of revenue maximizing auctions. We show that depending on the shape of outside options, sometimes an optimal mechanism will allocate the objects in an ex-post efficient way, and other times, buyers will obtain objects more often than it is efficient. Our characterization rings a bell of caution. Modeling buyers outside options as being independent of their private information, is with loss of generality and can lead to quite misleading intuitions. Our solution procedure can be useful also in other models where type-dependent outside options arise endogenously, because, for instance, buyers can collude or because there are competing sellers. Type-Dependent Outside Options: JEL D44, C7, C72. |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:edj:ceauch:231&r=gth |
| By: | Philippe Jehiel; Oliver Compte |
| Date: | 2007–09–07 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:122247000000001552&r=gth |
| By: | Philippe Jehiel |
| Date: | 2007–09–07 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:122247000000001547&r=gth |
| By: | Nicolás Figueroa; Vasiliki Skreta |
| Abstract: | This paper considers a general optimal auction problem, with many goods and with a buyer’s utility that can depend non-linearly in his type. We point out that incentive compatibility constraints may be binding even if virtual utilities are strictly increasing in the buyer’s type. More importantly, optimal mechanisms may involve randomizations between different allocations. |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:edj:ceauch:232&r=gth |
| By: | Tibor Neugebauer; Javier Perote; Ulrich Schmidt; Malte Loos |
| Abstract: | In the recent literature, several hypotheses have been put forward in order to explain the decline of contributions in repeated public good games. We present results of an experiment which allows to evaluate these hypotheses. The main characteristics of our experimental design are a variation of information feedback and an elicitation of individual beliefs about others’ contributions. Altogether, our data support the hypothesis of conditional cooperation with a selfish bias. |
| Keywords: | experimental economics, information feedback, public goods, voluntary contributions, conditional cooperation |
| JEL: | C72 C92 H41 |
| Date: | 2007–09 |
| URL: | http://d.repec.org/n?u=RePEc:kie:kieliw:1376&r=gth |
| By: | Vincent Anesi (University of Nottingham) |
| Abstract: | Most political and economic theorists point to moral hazard in teams as the main obstacle to lobbies' collective action. In this paper, we address this important issue with a coalition-formation game. In the process of doing so, we characterize equilibrium lobby structures both in the absence and in the presence of moral hazard. Three notable results emerge from such an exercise: (i) an equilibrium lobby structure exists under both specications of the model, (ii) moral hazard in teams may raise large groups' equilibrium lobby size, and (iii) it may also raise the total contribution to lobbying of large groups with low organizational costs. |
| Keywords: | Collective action, Moral hazard in teams, Lobby formation, Free-rider problem |
| JEL: | C72 D72 H41 |
| Date: | 2007–08 |
| URL: | http://d.repec.org/n?u=RePEc:cdx:dpaper:2007-04&r=gth |
| By: | Flavia Cortelezzi; Giovanni Villani |
| Abstract: | Aim of this paper is to analyse the equilibrium strategies of two firms investing in a new technology, when the probability of successful implementation is uncertain and market shares are asymmetric. In particular, we are able to consider three key feature of a new technology adoption. First, it is, at least partially, irreversible. Second, once realized, there is uncertainty about the probability of a successful implementation. Third, the profit flow generated by such an investment is subject to uncertainty according to the evolution of demand function. The first firm to enter the market sustaines the investment cost earlier, but can benefit of a higher market share with respect to the competitor. The follower has just to decide if and when realize the investment. He benefits from the resolution of uncertainty, but he suffers of a reduction in its market share. Using the method of option pricing theory, we address this issue at two levels. First, we model the investment decision of a non-cooperative firm (decentralised case) as a dynamic stochastic game. Then, we solve for the sequential monopolist as a benchmark case. We find the interaction of pre-emption and uncertainty can actually hasten, rather than delay, investment, contrary to the usual presumption. |
| Keywords: | Real Options; Stopping Timing Game, Asymmetric Demand. |
| JEL: | C73 G13 |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:ufg:qdsems:14-2007&r=gth |