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on Game Theory |
| By: | Markus Kinateder |
| Abstract: | Delayed perfect monitoring in an infinitely repeated discounted game is modelled by letting the players form a connected and undirected network. Players observe their immediate neighbors' behavior only, but communicate over time the repeated game's history truthfully throughout the network. The Folk Theorem extends to this setup, although for a range of discount factors strictly below 1, the set of sequential equilibria and the corresponding payoff set may be reduced. A general class of games is analyzed without imposing restrictions on the dimensionality of the payoff space. This and the bilateral communication structure allow for limited results under strategic communication only. As a by-product this model produces a network result; namely, the level of cooperation in this setup depends on the network's diameter, and not on its clustering coefficient as in other models. |
| Keywords: | Repeated Game, Network, Delayed Perfect Monitoring, Communication |
| JEL: | C72 C73 L14 |
| Date: | 2006–11–23 |
| URL: | http://d.repec.org/n?u=RePEc:aub:autbar:674.06&r=gth |
| By: | Josef Hofbauer (University College London, Department of Mathematics); Jörg Oechssler (University of Heidelberg, Department of Economics) |
| Abstract: | In John Nash’s proofs for the existence of (Nash) equilibria based on Brouwer’s theorem, an iteration mapping is used. A continuous- time analogue of the same mapping has been studied even earlier by Brown and von Neumann. This differential equation has recently been suggested as a plausible boundedly rational learning process in games. In the current paper we study this Brown-von Neumann-Nash dynamics for the case of continuous strategy spaces. We show that for continuous payoff functions, the set of rest points of the dynamics coincides with the set of Nash equilibria of the underlying game. We also study the asymptotic stability properties of rest points. While strict Nash equilibria may be unstable, we identify sufficient conditions for local and global asymptotic stability which use concepts developed in evolutionary game theory. |
| Keywords: | learning in games, evolutionary stability, BNN |
| JEL: | C70 C72 |
| Date: | 2005–12 |
| URL: | http://d.repec.org/n?u=RePEc:awi:wpaper:0424&r=gth |
| By: | Amparo Urbano (Universitat de València); Penélope Hernández (Universidad de Alicante) |
| Abstract: | This paper is a note on how Information Theory and Codification Theory are helpful in the computational design both of communication protocols and strategy sets in the framework of finitely repeated games played by boundedly rational agents. More precisely, we show the usefulness of both theories to improve the existing automata bounds of Neyman¿s (1998) work on finitely repeated games played by finite automata. |
| Keywords: | Complexity, codification, repeated games, finite automata |
| JEL: | C73 C72 |
| Date: | 2007–01 |
| URL: | http://d.repec.org/n?u=RePEc:ivi:wpasad:2006-28&r=gth |
| By: | Gary Bornstein |
| Date: | 2007–01–12 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:321307000000000739&r=gth |
| By: | Kirchkamp Oliver; Reiss J. Philipp; Sadrieh Abdolkarim (METEOR) |
| Abstract: | We introduce a new method of varying the risk that bidders face in first-price private value auctions. We find that decreasing bidders’ risk significantly reduces the degree of overbidding relative to the risk-neutral Bayesian-Nash equilibrium prediction. This implies that risk affects bidding behavior as generally expected in auction theory. While resolving a long-standing debate on the effect of risk on auction behavior, our results give rise to a new puzzle. As risk is diminished and overbidding decreases for most of the value range, a significant degree of underbidding sets in for very low values |
| Keywords: | Economics (Jel: A) |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2006058&r=gth |
| By: | Roy Chowdhury, Prabal |
| Abstract: | We examine a simple model of collusion under a single-object second-price auction. Under the appropriate parameter conditions, in particular as long as collusion is neither too easy, nor too difficult, we find that the optimal policy involves both an effective ceiling, as well as a reserve price. |
| Keywords: | Auctions; ceilings; collusion; reserve prices. |
| JEL: | D44 C72 |
| Date: | 2006–12 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:1503&r=gth |
| By: | Peter Dürsch (University of Heidelberg, Department of Economics); Albert Kolb (University of Bonn, Department of Economics); Jörg Oechssler (University of Heidelberg, Department of Economics); Burkhard C. Schipper (University of California, Department of Economics) |
| Abstract: | We use an experiment to explore how subjects learn to play against computers which are programmed to follow one of a number of standard learning algorithms. The learning theories are (unbeknown to subjects) a best response process, fictitious play, imitation, reinforcement learning, and a trial & error process. We test whether subjects try to influence those algorithms to their advantage in a forward-looking way (strategic teaching). We find that strategic teaching occurs frequently and that all learning algorithms are subject to exploitation with the notable exception of imitation. The experiment was conducted, both, on the internet and in the usual laboratory setting. We find some systematic differences, which however can be traced to the different incentives structures rather than the experimental environment. |
| Keywords: | learning; fictitious play; imitation; reinforcement; trial & error; strategic teaching; Cournot duopoly; experiments; internet. |
| JEL: | C72 C91 C92 D43 L13 |
| Date: | 2005–10 |
| URL: | http://d.repec.org/n?u=RePEc:awi:wpaper:0423&r=gth |
| By: | Irit Nowik; Idan Segev; Shmuel Zamir |
| Abstract: | Game theory is usually applied to biology through evolutionary games. However, many competitive processes in biology may be better understood by analyzing them on a shorter time-scale than the time-course considered in evolutionary dynamics. Instead of the change in the "fitness" of a player, which is the traditional payoff in evolutionary games, we define the payoff function, tailored to the specific questions addressed. In this work we analyze the developmental competition that arises between motoneurons innervating the same muscle. The "size principle" - a fundamental principle in the organization of the motor system, stating that motoneurons with successively higher activation-threshold innervate successively larger portions of the muscle - emerges as a result of this competition. We define a game, in which motoneurons compete to innervate a maximal number of muscle-fibers. The strategies of the motoneurons are their activation-thresholds. By using a game theoretical approach we succeed to explain the emergence of the size principle and to reconcile seemingly contradictory experimental data on this issue. The evolutionary advantage of properties as the size principle, emerging as a consequence of competition rather than being genetically hardwired, is that it endows the system with adaptation capabilities, such that the outcome may be fine-tuned to fit the environment. In accordance with this idea the present study provides several experimentally-testable predictions regarding the magnitude of the size principle in different muscles. |
| Date: | 2006–12 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp440&r=gth |