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on Game Theory |
| By: | V. Bhaskar (Department of Economics, University College, London); George J. Mailath (Department of Economics, University of Pennsylvania); Stephen Morris (Department of Economics, Princeton University) |
| Abstract: | We study perfect information games with an infinite horizon played by an arbitrary number of players. This class of games includes infinitely repeated perfect information games, repeated games with asynchronous moves, games with long and short run players, games with overlapping generations of players, and canonical non-cooperative models of bargaining. We consider two restrictions on equilibria. An equilibrium is purifiable if close by behavior is consistent with equilibrium when agents’ payoffs at each node are perturbed additively and independently. An equilibrium has bounded recall if there exists K such that at most one player’s strategy depends on what happened more than K periods earlier. We show that only Markov equilibria have bounded memory and are purifiable. Thus if a game has at most one long-run player, all purifiable equilibria are Markov. |
| Keywords: | Markov, bounded recall, purification |
| JEL: | C72 C73 |
| Date: | 2009–08–05 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:09-029&r=gth |
| By: | Richard Cornes; Roger Hartley |
| Abstract: | A game is fully aggregative if payoffs and marginal payoffs depend only on a player's own strategy and a function of the strategy profile which is common to all players. We characterize the form which this function must take in such a game and show that the game will be strategically equivalent to another game in which the function is the simple sum of strategies. |
| JEL: | C72 |
| Date: | 2009–08 |
| URL: | http://d.repec.org/n?u=RePEc:acb:cbeeco:2009-505&r=gth |
| By: | Christiane Ernst; Christian Thöni |
| Abstract: | We report results from experimental first-price, sealed-bid, all-pay auctions for a good with a common and known value. We observe bidding strategies in groups of two and three bidders and under two extreme information conditions. As predicted by the Nash equilibrium, subjects use mixed strategies. In contrast to the prediction under standard assumptions bids are drawn from a bimodal distribution: very high and very low bids are much more frequent than intermediate bids. Standard risk preferences cannot account for our results. However, bidding behavior is consistent with the predictions of a model with reference dependent preferences as proposed by the prospect theory. |
| Keywords: | All-pay Auction; Prospect Theory, Experiment |
| JEL: | D44 D72 D80 C91 |
| Date: | 2009–08 |
| URL: | http://d.repec.org/n?u=RePEc:usg:dp2009:2009-25&r=gth |
| By: | Rodrigo Velez (Texas A&M University); William Thomson (University of Rochester) |
| Abstract: | We consider the problem of fairly allocating a bundle of infinitely divisible commodities among a group of agents with "classical" preferences. We propose to measure an agent's "sacrifice" at an allocation by the size of the set of feasible bundles that the agent prefers to her consumption. As a solution, we select the allocations at which sacrifices are equal across agents and this common sacrifice is minimal. We then turn to the manipulability of this solution. In the tradition of Hurwicz (1972, Decision and Organization, U. Minnesota Press), we identify the equilibrium allocations of the manipulation game associated with this solution when all commodities are normal: (i) for each preference profile, each equal-division constrained Walrasian allocation is an equilibrium allocation; (ii) conversely, each equilibrium allocation is equal-division constrained Walrasian. (iii) Furthermore, we show that if normality of goods is dropped, then equilibrium allocations may not be efficient. |
| Keywords: | equal-sacrifice rule, manipulation game, equal-division Walrasian solution. |
| Date: | 2009–08 |
| URL: | http://d.repec.org/n?u=RePEc:roc:rocher:552&r=gth |
| By: | John Duggan (W. Allen Wallis Institute of Political Economy, 107 Harkness Hall, University of Rochester, Rochester, NY 14627-0158); Tasos Kalandrakis (W. Allen Wallis Institute of Political Economy, 107 Harkness Hall, University of Rochester, Rochester, NY 14627-0158) |
| Abstract: | We develop and implement a collocation method to solve for an equilibrium in the dynamic legislative bargaining game of Duggan and Kalandrakis (2008). We formulate the collocation equations in a quasi-discrete version of the model, and we show that the collocation equations are locally Lipchitz continuous and directionally differentiable. In numerical experiments, we successfully implement a globally convergent variant of Broyden's method on a preconditioned version of the collocation equations, and the method economizes on computation cost by more than 50% compared to the value iteration method. We rely on a continuity property of the equilibrium set to obtain increasingly precise approximations of solutions to the continuum model. We showcase these techniques with an illustration of the dynamic core convergence theorem of Duggan and Kalandrakis (2008) in a nine-player, two-dimensional model with negative quadratic preferences. |
| Date: | 2009–08 |
| URL: | http://d.repec.org/n?u=RePEc:roc:wallis:wp60&r=gth |
| By: | Hertel, Jo; Smith, John |
| Abstract: | We model a game similar to the interaction between an academic advisor and advisee. Like the classic cheap talk setup, an informed player sends information to an uninformed receiver who is to take an action which affects the payoffs of both sender and receiver. However, unlike the classic cheap talk setup, the preferences regarding the receiver's actions are identical for both sender and receiver. Additionally, the sender incurs a communication cost which is increasing in the complexity of the message sent. We characterize the resulting equilibria. Under an additional out-of-equilibrium condition (Condition L), if preferences for sender and receiver are identical then the only equilibria are the most informative, feasible ones. A similar result appears in Chen, Kartik and Sobel (2008) when their No Incentive to Separate (NITS) condition is applied to the case where communication is costless but preferences diverge. Additionally, we model the competency of the advisee by the probability that the action is selected by mistake. We show that the informativeness of the sender is decreasing in the likelihood of the mistake. When the preferences between players diverge and when there are communication costs, we are not guaranteed uniqueness and we provide an example where an increase in communication costs can improve communication. |
| Keywords: | complexity; communication; cheap talk |
| JEL: | D82 D83 C72 |
| Date: | 2009–08–22 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:17056&r=gth |
| By: | Elisabeth Gugl (Department of Economics, University of Victoria); Justin Leroux (HEC Montéral and CIRPÉE) |
| Abstract: | We consider an n-person economy in which efficiency is independent of distribution but the cardinal properties of the agents’ utility functions preclude transferable utility (a property we call “Almost TU”). We show that Almost TU is a necessary and sufficient condition for all agents to either benefit jointly or suffer jointly with any change in production possibilities under well-behaved generalized utilitarian bargaining solutions (of which the Nash Bargaining and the utilitarian solutions are special cases). We apply the result to household decision-making in the context of the Rotten Kid Theorem and in evaluating a change in family taxation. |
| Keywords: | Axiomatic bargaining, Solidarity, Transferable utility, Family taxation, Rotten Kid Theorem |
| JEL: | C71 D13 D63 |
| Date: | 2009–08–22 |
| URL: | http://d.repec.org/n?u=RePEc:vic:vicddp:0903&r=gth |
| By: | Margherita Comola; Marcel Fafchamps |
| Abstract: | The literature has shown that network architecture depends crucially on whether links are formed unilaterally or bilaterally, that is, on whether the consent of both nodes is required for a link to be formed. We propose a test of whether network data is best seen as an actual link or willingness to link and, in the latter case, whether this link is generated by an unilateral or bilateral link formation process. We illustrate this test using survey answers to a risk-sharing question in Tanzania. We find that the bilateral link formation model fits the data better than the unilateral model, but the data are best interpreted as willingness to link rather than an actual link. We then expand the model to include self-censoring and find that models with self-censoring fit the data best. |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:pse:psecon:2009-30&r=gth |
| By: | Correani, L; Di Dio, F; Garofalo, G |
| Abstract: | In this paper, we analyze the role of cooperation between firms through a model of growth and social capital. In a growth model à la Solow we incorporate the set of resources that a relational network has at its disposals, as a distinct production factor, and thus examine its dissemination through evolutionary type processes in firm interactions. Dynamic analysis of the model demonstrates that cooperation is able to increase the productivity of factors, fostering a higher rate of growth in the long term. The most significant result is that scarcity of social capital can produce a general collapse of the economic system in areas in which long term growth is usually sustained by the learning by doing and spillover of knowledge phenomena. This conclusion leads to reconsider the role of local development economic policies that should concentrate on activities that promote repeated interaction between firms proven to be cooperative or that encourage the formation of technological consortia. |
| Keywords: | Economic growth; Social capital; Networks; Evolutionary games |
| JEL: | C71 O43 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:17043&r=gth |