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on Game Theory |
| By: | Reinhard Selten; Thorsten Chmura |
| Abstract: | Four stationary concepts for completely mixed 2x2 games are experimentally compared: Nash equilibrium, quantal response equilibrium, sample-7 equilibrium and impulse balance equilibrium. Experiments on 12 games, 6 constant sum games and 6 non-constant sum games were run with 12 independent subject groups for each constant sum game and 5 independent subject groups for each nonconstant sum game. Each independent subject group consisted of 4 payers 1 and four players 2 interacting anonymously over 200 periods with random matching. The games were selected to yield a reasonably wide distribution over the parameter space. The comparison of the four theories shows that the order of performance from best to worst is as follows: impulse balance equilibrium, sample-7 equilibrium, quantal response equilibrium, Nash equilibrium. The new concepts of sample-7 equilibrium and impulse balance equilibrium are explained in the text. |
| Date: | 2005–11 |
| URL: | http://d.repec.org/n?u=RePEc:bon:bonedp:bgse33_2005&r=gth |
| By: | Pedro Rey-Biel (Universidad Autónoma Barcelona) |
| Abstract: | We report experimental results on one-shot two person 3x3 constant sum games played by non-economists without previous experience in the laboratory. Although strategically our games are very similar to previous experiments in which game theory predictions fail dramatically, 80% of actions taken in our experiment coincided with the unique Nash equilibrium in pure strategies and 73% of actions were best responses to elicited beliefs. We argue how social preferences, presentation effects and belief elicitation procedures may influence the way subjects play in simple but non trivial games and explain differences with previous work. |
| Keywords: | Experiments Constant Sum Games Stated Beliefs |
| JEL: | C9 |
| Date: | 2005–12–06 |
| URL: | http://d.repec.org/n?u=RePEc:wpa:wuwpex:0512003&r=gth |
| By: | Dino Gerardi (Cowles Foundation, Yale University); Roger B. Myerson (Dept. of Economics, University of Chicago) |
| Abstract: | We study the effects of communication in Bayesian games when the players are sequentially rational but some combinations of types have zero probability. Not all communication equilibria can be implemented as sequential equilibria. We define the set of strong sequential equilibria (SSCE) and characterize it. SSCE differs from the concept of sequential communication equilibrium (SCE) defined by Myerson (1986) in that SCE allows the possibility of trembles by the mediator. We show that these two concepts coincide when there are three or more players, but the set of SSCE may be strictly smaller than the set of SCE for two-player games. |
| Keywords: | Bayesian games, Communication, Communication equilibrium, Sequential communication equilibrium |
| JEL: | C72 D82 |
| Date: | 2005–12 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1542&r=gth |
| By: | Dinah Rosenberg; Eilon Solan; Nicolas Vieille |
| Date: | 2004–11–28 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levarc:122247000000000704&r=gth |
| By: | Velzen,Bas van (Tilburg University, Center for Economic Research) |
| Abstract: | In this paper we introduce the class of simple combinatorial optimisation cost games, which are games associated to {0, 1}-matrices. A coalitional value of a combinatorial optimisation game is determined by solving an integer program associated with this matrix and the characteristic vector of the coalition. For this class of games, we will characterise core stability and totally balancedness. We continue by characterising exactness and largeness. Finally, we conclude the paper by applying our main results to minimum colouring games and minimum vertex cover games. |
| Keywords: | totally balancedness;largeness;exactness; games;optimization;stability |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2005118&r=gth |
| By: | Mathevet, Laurent |
| Date: | 2005–12 |
| URL: | http://d.repec.org/n?u=RePEc:clt:sswopa:1243&r=gth |
| By: | Ronald M. Harstad (Department of Economics, University of Missouri-Columbia) |
| Abstract: | Potential bidders respond to a seller's choice of auction mechanism for a common-value or affiliated-values asset by endogenous decisions whether to incur a participation cost (and observe a private signal), or forego competing. Privately informed participants decide whether to incur a bid-preparation cost and pay an entry fee, or cease competing. Auction rules and information flows are quite general; participation decisions may be simultaneous or sequential. The resulting revenue identity for any auction mechanism implies that optimal auctions are allocatively efficient; a nontrivial reserve price is revenue-inferior for any common-value auction. Optimal auctions are otherwise contentless: any auction that sells without reserve becomes optimal by adjusting any one of the continuous, spanning parameters, e.g., the entry fee. Seller.s surplus-extracting tools are now substitutes, not complements. Many econometric studies of auction markets are seen to be flawed in their identification of the number of bidders. |
| Keywords: | Optimal Auctions, Endegenous Bidder Participation, Affiliated-Values, Common-Value Auctions, Surplus-Extracting Devices |
| JEL: | D44 D82 C72 |
| Date: | 2005–12–07 |
| URL: | http://d.repec.org/n?u=RePEc:umc:wpaper:0518&r=gth |
| By: | Ana, MAULEON; José, SEMPERE-MONERRIS; Vincent, VANNETELBOSCH |
| Abstract: | We study the endogenous formation of networks between manufacturers of differentiated goods and multi-product retailers who interact in a successive duopoly. Joint consent is needed to establish and/or maintain a costly link between a manufacturer and a retailer. We find that only three distribution networks are stable for particular values of the degree of product differentiation and link costs : (i) the non-exclusive distribtion & non-exclusive dealing network in which both retailers distribute both products is stable for intermediate degree of product differentiation and small link costs; (ii) the exclusive distribution & exclusive dealing network in which each retailer distributes a different product is stable for low degrees of product differentiation; (iii) the mixed distribution network in which one retailer distributes both products while the other retailer sells only one is stable for high degrees of product differentiation and large link costs. We show that the distribution networks that maximize social welfare are not necessarily stable. Thus, a conflict between stability and social welfare is likely to occur, even more if the degree of product differentiation is either low or high. |
| Keywords: | Networks; Retailers; Manufacturers |
| JEL: | C70 L13 L20 J50 J52 |
| Date: | 2005–06–15 |
| URL: | http://d.repec.org/n?u=RePEc:ctl:louvec:2005036&r=gth |
| By: | David K Levine |
| Date: | 2005–12–04 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levarc:618897000000001000&r=gth |
| By: | Anirban Kar, Indrajit Ray and Robedrto Serrano |
| Abstract: | We view achieving a particular correlated equilibrium distribution for a normal form game as an implementation problem. We show, using a parametric version of the two-person Chicken game and a wide class of correlated equilibrium distributions, that a social choice function that chooses a particular correlated equilibrium distribution from this class does not satisfy the Maskin monotonicity condition and therefore can not be fully implemented in Nash equilibrium. |
| Keywords: | Correlated Equilibrium Distribution, Implementation, Monotonicity |
| JEL: | C72 |
| Date: | 2005–11 |
| URL: | http://d.repec.org/n?u=RePEc:bir:birmec:05-18&r=gth |
| By: | Subhadip Chakrabarti; Robert P. Gilles |
| Abstract: | A network payoff function assigns a utility to all participants in a (social) network. In this paper we discuss properties of such network payoff functions that guarantee the existence of certain types of pairwise stable networks and the convergence of certain network formation processes. In particular we investigate network payoff functions that admit an exact network potential or an ordinal network potential. We relate these network potentials to exact and ordinal potentials of a non-cooperative network formation game based on consent in link formation. Our main results extend and strengthen the current insights in the literature on game theoretic approaches to social network formation. |
| Keywords: | Network formation; pairwise stability; potential functions |
| JEL: | C72 C79 D85 |
| Date: | 2005–10 |
| URL: | http://d.repec.org/n?u=RePEc:bon:bonedp:bgse28_2005&r=gth |
| By: | Peter Dürsch; Albert Kolb; Jörg Oechssler; Burkhard C. Schipper |
| 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:bon:bonedp:bgse31_2005&r=gth |
| By: | John Janmaat (Acadia University) |
| Abstract: | The ultimatum game experiment has a long history in experimental economics. In-vivo ultimatum like strategic settings often involve uncertain rejection and payoff reversals. This paper presents the results of an ultimatum like experiment extended to reflect characteristics of a shared international river, in particular where a downstream nation has the potentially payoff reversing strategy option of a military strike. Subjects implicitly split an endowment between water consuming and security enhancing investments, where relative security investments determine the probability of the payoff reversal, with one subject being able to purchase a gamble to reverse the payoffs. Maximin, folk, and Nash solutions are compared, with results suggesting that behavior is responding to folk theorem like incentives. Dynamic analyses support this by showing no significant relationship between the gamble choice and its single period rationality. |
| Keywords: | Resource Economics, Peace Economics, Experimental Economics, Applied Game Theory |
| JEL: | C7 C9 N4 Q2 |
| Date: | 2005–12–07 |
| URL: | http://d.repec.org/n?u=RePEc:wpa:wuwpex:0512004&r=gth |
| By: | Kets,Willemien; Voorneveld,Mark (Tilburg University, Center for Economic Research) |
| Abstract: | Behavioral economics provides several motivations for the common observation that agents appear somewhat unwilling to deviate from recent choices. More recent choices can be more salient than other choices, or more readily available in the agent's mind. Alternatively, agents may have formed habits, use rules of thumb, or lock in on certain modes of behavior as a result of learning by doing. This paper provides discrete-time adjustment processes for strategic games in which players display precisely such a bias towards recent choices. In addition, players choose best replies to beliefs supported by observed play in the recent past, in line with much of the literature on learning. These processes eventually settle down in the minimal prep sets of Voorneveld [Games Econ. Behav. 48 (2004) 403-414, and Games Econ. Behav. 51 (2005) 228-232]. |
| Keywords: | adjustment;minimal prep sets;availability bias;salience;rules of thumb; learning |
| JEL: | C72 D83 |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2005117&r=gth |
| By: | Aviad Heifetz; Martin Meier; Burkhard C. Schipper |
| Abstract: | Heifetz, Meier and Schipper (2005) introduced a generalized state-space model that allows for non-trivial unawareness among several individuals and strong properties of knowledge. We show that this generalized state-space model arises naturally if states consist of maximally consistent sets of formulas in an appropriate logical formulation. |
| Keywords: | unawareness, awareness, knowledge, interactive epistemology, modal logic, lack of conception, bounded perception |
| JEL: | C70 C72 D80 D82 |
| Date: | 2005–09 |
| URL: | http://d.repec.org/n?u=RePEc:bon:bonedp:bgse23_2005&r=gth |