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on Game Theory |
| By: | Frank H. Page, Jr. (Department of Finance, University of Alabama); Myrna H. Wooders (Department of Economics, Vanderbilt University) |
| Abstract: | We make four main contributions to the theory of network formation. (1) The problem of network formation with farsighted agents can be formulated as an abstract network formation game. (2) In any farsighted network formation game the feasible set of networks contains a unique, finite, disjoint collection of nonempty subsets having the property that each subset forms a strategic basin of attraction. These basins of attraction contain all the networks that are likely to emerge and persist if individuals behave farsightedly in playing the network formation game. (3) A von Neumann Morgenstern stable set of the farsighted network formation game is constructed by selecting one network >from each basin of attraction. We refer to any such von Neumann-Morgenstern stable set as a farsighted basis. (4) The core of the farsighted network formation game is constructed by selecting one network >from each basin of attraction containing a single network. We call this notion of the core, the farsighted core. We conclude that the farsighted core is nonempty if and only if there exists at least one farsighted basin of attraction containing a single network. To relate our three equilibrium and stability notions (basins of attraction, farsighted basis, and farsighted core) to recent work by Jackson and Wolinsky (1996), we define a notion of pairwise stability similar to the Jackson-Wolinsky notion and we show that the farsighted core is contained in the set of pairwise stable networks. Finally, we introduce, via an example, competitive contracting networks and highlight how the analysis of these networks requires the new features of our network formation model. |
| Date: | 2005–04 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:0509&r=gth |
| By: | Edward Cartwright (Department of Economics, Keynes College, University of Kent); Myrna Wooders (Department of Economics, Vanderbilt University) |
| Abstract: | Treating games of incomplete information with countable sets of actions and types and finite but large player sets we demonstrate that for every mixed strategy profile there is a pure strategy profile that is 'epsilon-equivalent'. Our framework introduces and exploits a distinction between crowding attributes of players (their external effects on others) and their taste attributes (their payoff functions and any other attributes that are not directly relevant to other players). The main assumption is a 'large game' property, dictating that the actions of relatively small subsets of players cannot have large effects on the payoffs of others Since it is well known that, even allowing mixed strategies, with a countable set of actions a Nash equilibrium may not exist, we provide an existence of equilibrium theorem. The proof of existence relies on a relationship between the 'better reply security' property of Reny (1999) and a stronger version of the large game property. Our purification theorem are based on a new mathematical result, of independent interest, applicable to countable strategy spaces. |
| Date: | 2005–04 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:0511&r=gth |
| By: | J. Carlos Gonzalez-Pimienta; Cristian M. Litan |
| Abstract: | We identify the maximal set of finite extensive forms for which the sets of subgame perfect and sequential equilibrium strategies coincide for any possible assignment of the payoff function. We also identify the maximal set of finite extensive forms for which the outcomes induced by the two solution concepts coincide. |
| Date: | 2005–04 |
| URL: | http://d.repec.org/n?u=RePEc:cte:werepe:we052616&r=gth |
| By: | Edward Cartwright (Department of Economics, Keynes College, University of Kent); Myrna Wooders (Department of Economics, Vanderbilt University) |
| Abstract: | Kalai (2002) demonstrates that in semi anonymous Bayesian games with sufficiently many players any Bayesian equilibrium is approximately ex-post Nash. In this paper we demonstrate that the existence of an approximate expost Nash property implies a purification result of the standard sort for the original Bayesian game. We also provide an example showing that the bound we obtain on the distance of a purified approximate equilibrium from an exact equilibrium is tight. |
| Date: | 2005–04 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:0512&r=gth |
| By: | Voorneveld,Mark; Kets,Willemien; Norde,Henk (Tilburg University, Center for Economic Research) |
| Abstract: | Norde et al. [Games Econ. Behav. 12 (1996) 219] proved that none of the equilibrium concepts in the literature on equilibrium selection in finite strategic games satisfying existence is consistent. A transition to set-valued solution concepts overcomes the inconsistency problem: there is a multiplicity of consistent set-valued solution concepts that satisfy nonemptiness and recommend utility maximization in one-player games. The minimal curb sets of Basu and Weibull [Econ. Letters 36 (1991) 141] constitute one such solution concept; this solution concept is axiomatized in this article. |
| JEL: | C72 |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200553&r=gth |
| By: | Fan-chin Kung (Academia Sinica) |
| Abstract: | We study how individuals divide themselves into coalitions and choose a public alternative for each coalition. When preferences have consecutive support and coalition feasible sets are positively population- responsive, the proposed consecutive benevolence solution generates allocations belonging to the coalition structure core and that are also Tiebout equilibria. However, when each coalition follows a single-valued collective decision rule, the coalition structure core may be empty. Our results show that if individual preferences are, in a sense, similar and if members can be as well off when a coalition enlarges, then a stable formation of collective decision-making units can be guaranteed. A predetermined decision rule makes coalitions less stable. |
| JEL: | C62 C71 D71 |
| Date: | 2005–05–05 |
| URL: | http://d.repec.org/n?u=RePEc:wpa:wuwpga:0505002&r=gth |
| By: | Bergh, Andreas (Department of Economics, Lund University); Engseld, Peter (Department of Economics, Lund University) |
| Abstract: | The standard method when analyzing the problem of cooperation using evolutionary game theory is to assume that people are randomly matched against each other in repeated games. In this paper we discuss the implications of allowing agents to have preferences over possible opponents. We model reputation as a noisy observation of actual propensity to cooperate and illustrate how reputation based choice of opponents can explain both the emergence and deterioration of cooperation. We show that empirical and experimental evidence of cooperation is consistent with our hypothesis that people behave so as to minimize the risk of damaging their reputation as nice, cooperative persons. |
| Keywords: | Cooperation; Prisoners Dilemma; Signaling; Reputation; Altruism; Institutions |
| JEL: | C70 C90 |
| Date: | 2005–04–28 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:lunewp:2005_027&r=gth |
| By: | Francesco De Sinopoli; Giovanna Iannantuoni |
| Abstract: | Most of the voting models restrict themselves to the analysis of symmetric equilibria, i.e. equilibria in which ‘similar’ voters make ‘similar’ voting decisions. In this paper we investigate this assumption under costly plurality voting. In any pure strategy equilibrium, if two active voters have the same preference order over candidates, they do vote for the same candidate. However, as an example shows, this type of result cannot be hoped for mixed strategies equilibria. |
| Keywords: | Strategic Voting, Symmetric Equilibria |
| JEL: | C72 D72 |
| Date: | 2005–05 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:0521&r=gth |
| By: | Blume,Andreas; DeJong,Douglas V.; Maier,Michael (Tilburg University, Center for Economic Research) |
| Abstract: | In common-interest spatial-dispersion games the agents common goal is to choose distinct locations. We experimentally investigate the role of cognition in such games and compare it with the role of cognition in spatial matching games. In our setup cognition matters because agents may be differentially aware of the dispersion opportunities that are created by the history of the game. We ask whether cognitive constraints limit the agents ability to achieve dispersion and, if there is dispersion, whether these constraints affect the mode by which agents achieve dispersion. Our main finding is that strategic interaction magnifies the role of cognitive constraints. Specifically, with cognitive constraints, pairs of agents fail to solve a dispersion problem that poses little or no problem for individual agents playing against themselves. When we remove the cognitive constraints in our design, pairs of agents solve the same problem just as well as individuals do. In addition, we find that when playing against themselves agents do not change the mode by which they solve the dispersion problem when our design removes the cognitive constraints. |
| JEL: | C72 C92 |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200558&r=gth |
| By: | Blume,Andreas; DeJong,Douglas V.; Maier,Michael (Tilburg University, Center for Economic Research) |
| Abstract: | We experimentally investigate coordination games in which cognition plays an important role, i.e. where outcomes are affected by the agents level of understanding of the game and the beliefs they form about each others understanding. We ask whether and when repeated exposure permits agents to learn to improve cognition in a strategic setting. We find evidence for strategic sophistication being learned, generalized and promoted. Agents acquire strategic sophistication in simple settings. They may fail to do so in similar but more demanding settings. Given the opportunity, they transfer learning from the simple to the more demanding task. There is heterogeneity in sophistication. We find some evidence for sophisticated agents trying to spread sophistication early in the game, provided there is a long enough time horizon. |
| JEL: | C72 C92 |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200559&r=gth |
| By: | Andrew F. Daughety (Department of Economics and Law School, Vanderbilt University); Jennifer F. Reinganum (Department of Economics and Law School, Vanderbilt University) |
| Abstract: | We briefly review two basic models of settlement bargaining based on concepts from information economics and game theory. We then discuss how these models have been generalized to address issues that arise when there are more than two litigants with related cases. Linkages between cases can arise due to exogenous factors such as correlated culpability or damages, or they can be generated by discretionary choices on the part of the litigants themselves or by legal doctrine and rules of procedure. |
| Keywords: | Multiple litigants, externalities, asymmetric information |
| JEL: | K41 D82 C78 |
| Date: | 2005–04 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:0508&r=gth |