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on Game Theory |
| By: | Roberto Burguet; Ramon Caminal |
| Abstract: | We propose and analyze a new solution concept, the R solution, for three-person, transferable utility, cooperative games. In the spirit of the Nash Bargaining Solution, our concept is founded on the predicted outcomes of simultaneous, two-party negotiations that would be the alternative to the grand coalition. These possibly probabilistic predictions are based on consistent beliefs. We analyze the properties of the R solution and compare it with the Shapley value and other concepts. The R solution exists and is unique. It belongs to the bargaining set and to the core whenever the latter is not empty. In fact, when the grand coalition can simply execute one of the three possible bilateral trades, the R solution is the most egalitarian selection of the bargaining set. Finally, we discuss how the R solution changes important conclusions of several well known Industrial Organization models. |
| Keywords: | cooperative games, bargaining, endogenous fall-back options, consistent beliefs, R solution. |
| JEL: | C71 C78 L14 |
| Date: | 2010–11–17 |
| URL: | http://d.repec.org/n?u=RePEc:aub:autbar:854.10&r=gth |
| By: | Dan Kovenock; Brian Roberson; Roman M. Sheremeta |
| Abstract: | This paper experimentally examines behavior in a two-player game of attack and defense of a weakest-link network of targets, in which the attacker’s objective is to successfully attack at least one target and the defender’s objective is diametrically opposed .We apply two benchmark contest success functions (CSFs): the auction CSF and the lottery CSF. Consistent with the theoretical prediction, under the auction CSF, attackers utilize a stochastic “guerilla warfare” strategy - in which a single random target is attacked - more than 80% of the time. Under the lottery CSF, attackers utilize the stochastic guerilla warfare strategy almost 45% of the time, contrary to the theoretical prediction of an equal allocation of forces across the targets. |
| Keywords: | Colonel Blotto, conflict resolution, weakest-link, best-shot, multi-dimensional resource allocation, experiments |
| JEL: | C72 C91 D72 D74 |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:pur:prukra:1256&r=gth |
| By: | Bezalel Peleg; Peter Sudholter; Jose M. Zarzuelo |
| Abstract: | On several classes of n-person NTU games that have at least one Shapley NTU value, Aumann characterized this solution by six axioms: Non-emptiness, efficiency, unanimity, scale covariance, conditional additivity, and independence of irrelevant alternatives (IIA). Each of the first five axioms is logically independent of the remaining axioms, and the logical independence of IIA is an open problem. We show that for n = 2 the first five axioms already characterize the Shapley NTU value, provided that the class of games is not further restricted. Moreover, we present an example of a solution that satisfies the first 5 axioms and violates IIA for 2-person NTU games (N;V) with uniformly p-smooth V(N). |
| Date: | 2010–10 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp561&r=gth |
| By: | Massimiliano Landi (School of Economics, Singapore Management University); Mauro Sodini (Dipartimento di Statistica e Matematica Applicata all'Economia, Universita degli Studi di Pisa) |
| Abstract: | We propose an evolutionary analysis of a voting game where citizens have a preference for conformism that adds to the instrumental preference for the electoral outcome. Multiple equilibria arise, and some generate high turnout. Simulations of best response dynamics show that high turnout is asymptotically stable if conformism matters but its likelihood depends on the reference group for conformism: high turnout is more likely when voters care about their own group's choice, as this better overrides the free rider problem of voting games. Comparative statics on the voting cost distribution, the population's size or the groups' composition are also done. |
| Keywords: | Turnout, Turnout, coordination games, Poisson games, conformism, selection dynamics. |
| JEL: | D72 C72 C73 |
| Date: | 2010–11 |
| URL: | http://d.repec.org/n?u=RePEc:siu:wpaper:25-2010&r=gth |
| By: | Britz Volker (METEOR) |
| Abstract: | We propose a new model to study the role of commitment as a sourceof strategic bargaining power. Two impatient players bargain aboutthe division of a pie under a standard bargaining protocol indiscrete time with time-invariant recognition probabilities.Instantaneous utility is linear, but players discount the future bya constant factor. Before bargaining starts, a player can commit notto enter into any agreement which gives him less than some utilitylevel. This commitment is perfectly binding initially. However, onceso much time has passed that even receiving the entire pie wouldyield less than the committed level of utility, then the commitmentbecomes void. Intuitively, this simply means that no player canremain committed to something which has become impossible. We use aslight refinement of subgame-perfect equilibrium as a solutionconcept. If only one player can commit, then we find an immediateand efficient agreement on a division which gives the committedplayer (strictly) between one half and the entire pie, the exactallocation being determined uniquely by the recognitionprobabilities. If both players can commit sequentially before thebargaining starts, we find a unique equilibrium division with afirst--mover advantage. Finally, we consider a version of the gamewhere both players commit simultaneously before the bargainingstarts. In this case, there is a range of equilibrium divisions.However, in the limit as the discount factor goes to one, no playerobtains less than one third of the pie, even with arbitrarily smallproposal power. Somewhat surprisingly, the equal split emerges asthe only division supported by an equilibrium for any choice of thediscount factor and the recognition probabilities. |
| Keywords: | microeconomics ; |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2010056&r=gth |
| By: | Tang, Qianfeng |
| Abstract: | The Bayesian solution is a notion of correlated equilibrium proposed by Forges (1993), and hierarchies of beliefs over conditional beliefs are introduced by Ely and Pęski (2006) in their study of interim rationalizability. We study the connection between the two concepts. We say that two type spaces are equivalent if they represent the same set of hierarchies of beliefs over conditional beliefs. We show that the correlation embedded in equivalent type spaces can be characterized by partially correlating devices, which send correlated signals to players in a belief invariant way. Since such correlating devices also implement the Bayesian solution, we establish that the Bayesian solution is invariant across equivalent type spaces. |
| Keywords: | Games with incomplete information, Correlated equilibrium, The Bayesian solution, Common knowledge, Hierarchies of beliefs. |
| JEL: | C70 C72 |
| Date: | 2010–11–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:26811&r=gth |
| By: | Maria Gabriella Graziano (Università di Napoli Federico II and CSEF); Maria Romaniello (Seconda Università di Napoli) |
| Abstract: | We introduce von Neumann-Morgenstern solution concepts in market models involving the choice of a public project. We show that vN-M stable sets, suitably defined in connection to public goods provision, are consistent with results from bargaining via cartels. We find as necessary the assumption that stability is defined with respect to blocking procedures in which coalitions do not necessarily pay for the whole realization of the project, but only for a fraction of it and that costs are distributed uniformly in each corner of the market. Under this assumption, we obtain large games solutions by the finite ones via embedding procedures. Going further in the investigation of stable solutions, we define stable sets following the “sophisticated” approach suggested by Harsanyi (see [15] and [17]), proving that a sigma-sophisticated stable set corresponds to the solution in the associated payoff space. |
| Keywords: | Public project, sigma-core, von Neumann-Morgenstern sigma-stable set, sigma-sophisticated stable sets |
| JEL: | D51 D60 H41 |
| Date: | 2010–10–28 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:263&r=gth |
| By: | Berninghaus, Siegfried; Güth, Werner; Schosser, Stephan |
| Abstract: | In repeated Public Good Games contributions might be influenced by different motives. The variety of motives for deciding between (more or less) free-riding probably explains the seemingly endless tradition of theoretical and experimental studies of repeated Public Good Games. To more clearly distinguish the motives, we try to enrich the choice set by allowing players not only to contribute but also to locate their contribution to one of the player positions. The location choice affects what individual players gain, but not the overall efficiency of contributing, and allows for discrimination, e.g., rewarding and sanctioning co-players differently. Our experimental results show that adding location choice promotes voluntary cooperation, although discrimination itself has no signifficant effect on behavior. -- |
| Keywords: | Public Good Game,Neighborhood,Cooperation,Experimental Analysis |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:kitwps:11&r=gth |
| By: | David Rietzke; Brian Roberson |
| Abstract: | This paper examines the robustness of alliance formation in a three-player, two-stage game in which each of two players compete against a third player in disjoint sets of contests. Although the players with the common opponent share no common interests, we find that under the lottery contest success function (CSF) there exists a range of parameter configurations in which the players with the common opponent have incentive to form an alliance involving a pre-conflict transfer of resources. Models that utilize the lottery CSF typically yield qualitatively different results from those arising in models with the auction CSF (Fang 2002). However, under the lottery and the auction CSFs, the parameter configurations within which players with a common opponent form an alliance are closely related. Our results, thus, provide a partial robustness result for ‘enemy-of-my-enemy-is-my-friend’ alliances. |
| Keywords: | Alliance Formation, Contests, Economics of Alliances, Conflict |
| JEL: | C72 D74 |
| Date: | 2010–10 |
| URL: | http://d.repec.org/n?u=RePEc:pur:prukra:1258&r=gth |
| By: | Aner Sela (Department of Economics, Ben-Gurion University of the Negev, Israel); Eyal Erez |
| Abstract: | We study a round-robin tournament with n symmetric players where in each of the n-1 stages each of the players competes against a different player in the Tullock contest. Each player has a limited budget of effort that decreases within the stages proportionally to the effort he exerted in the previous stages. We show that when the prize for winning (value of winning) is equal between the stages, a player's effort is weakly decreasing over the stages. We also show how the contest designer can influence the players' allocation of effort by changing the distribution of prizes between the stages. In particular, we analyze the distribution of prizes over the stages that balance the effort allocation such that a player exerts the same effort over the different stages. In addition, we analyze the distribution of prizes over the stages that maximizes the players' expected total effort. |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:bgu:wpaper:1009&r=gth |
| By: | Massimo Morelli; Dominic Rohner |
| Abstract: | We examine how natural resource location, rent sharing and fighting capacities of different groups matter for ethnic conflict. A new type of bargaining failure due to multiple types of potential conflicts (and hence multiple threat points) is identified. The theory predicts conflict to be more likely when the geographical distribution of natural resources is uneven and when a minority group has better chances to win a secessionist rather than a centrist conflict. For sharing rents, resource proportionality is salient in avoiding secessions and strength proportionality in avoiding centrist civil wars. We present empirical evidence that is consistent with the model. |
| Keywords: | Natural Resources, Conflict, Strength Proportionality, Resource Proportionality, Secession, Bargaining Failure |
| JEL: | C72 D74 Q34 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:oxcrwp:050&r=gth |
| By: | Marie-Laure Cabon-Dhersin (Centre d'Economie de la Sorbonne - Paris School of Economics & Ecole normale supérieure de Cachan); Nathalie Etchart-Vincent (Centre d'Economie de la Sorbonne - Paris School of Economics & Ecole normale supérieure de Cachan) |
| Abstract: | Wording has been widely shown to affect decision making. In this paper, we investigate experimentally whether and to what extent, cooperative behaviour in a Game of Chicken may be impated by a very basic change in the labelling of the strategies. Our within-subject experimental design involves two treatments. The only difference between them is that we introduce either a socially-oriented wording ("I cooperate"/"I do not cooperate") or colours (red/blue) to designate strategies. The level of cooperation appears to be higher in the socially-oriented context, but only when the uncertainty as regards the type of the partner is manipulated, and especially among females. |
| Keywords: | Social dilemma, Game of Chicken, cooperation, wording effects, gender effects. |
| JEL: | C72 C92 |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:10080&r=gth |
| By: | Yakov Babichenko |
| Abstract: | We consider uncoupled dynamics (i.e., dynamics where each player knows only his own payoff function) that reach Pareto efficient and individually rational outcomes. We prove that the number of periods it takes is in the worst case exponential in the number of players. |
| Date: | 2010–10 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp562&r=gth |
| By: | Clara Ponsati; Santiago Sanchez-Pages |
| Abstract: | We propose an elementary theory of wars fought by fully rational contenders. Two parties play a Markov game that combines stages of bargaining with stages where one side has the ability to impose surrender on the other. Under uncertainty and incomplete information, in the unique equilibrium of the game, long confrontations occur: war arises when reality disappoints initial (rational) optimism, and it persist longer when both agents are optimists but reality proves both wrong. Bargaining proposals that are rejected initially might eventually be accepted after several periods of confrontation. We provide an explicit computation of the equilibrium, evaluating the probability of war, and its expected losses as a function of i) the costs of confrontation, ii) the asymmetry of the split imposed under surrender, and iii) the strengths of contenders at attack and defense. Changes in these parameters display non-monotonic effects. |
| Keywords: | Conflict, Income redistribution, Natives, Immigrants. |
| JEL: | C78 D74 |
| Date: | 2010–11–18 |
| URL: | http://d.repec.org/n?u=RePEc:edn:esedps:197&r=gth |
| By: | Michael R. Baye (Department of Business Economics and Public Policy, Indiana University Kelley School of Business); Dan Kovenock (Department of Economics, Tippie College of Business, University of Iowa); Casper G. de Vries (Tinbergen Institute and Erasmus University Rotterdam) |
| Abstract: | The Babylonian bridal auction, described by Herodotus, is regarded as one of the earliest uses of an auction in history. Yet, to our knowledge, the literature lacks a formal equilibrium analysis of this auction. We provide such an analysis for the two-player case with complete and incomplete information, and in so doing identify what we call the “Herodotus Paradox.” |
| JEL: | C72 D44 L0 |
| Date: | 2010–07 |
| URL: | http://d.repec.org/n?u=RePEc:iuk:wpaper:2010-16&r=gth |
| By: | Britz Volker; Herings Jean-Jacques; Predtetchinski Arkadi (METEOR) |
| Abstract: | Suppose that a firm has several owners and that the future is uncertain in the sense that one out of many different states of nature will realize tomorrow. An owner''s time preference and risk attitude will determine the importance he places on payoffs in the different states. It is a well--known problem in the literature that under incomplete asset markets, a conflict about the firm''s objective function tends to arise among its owners. In this paper, we take a new approach to this problem, which is based on non--cooperative bargaining. The owners of the firm play a bargaining game in order to choose the firm''s production plan and a scheme of transfers which are payable before the uncertainty about the future state of nature is resolved. We analyze the resulting firm decision in the limit of subgame--perfect equilibria in stationary strategies. Given the distribution of bargaining power, we obtain a unique prediction for a production plan and a transfer scheme. When markets are complete, the production plan chosen corresponds to the profit-maximizing production plan as in the Arrow-Debreu model. Contrary to that model, owners typically do use transfers to redistribute profits. When markets are incomplete, the production plan chosen is almost always different from the standard notion of competitive equilibrium and again owners use transfers to redistribute profits. Nevertheless, our results do support the Drèze criterion as the appropriate objective function of the firm. |
| Keywords: | microeconomics ; |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2010057&r=gth |
| By: | Eric Van den Steen (Harvard Business School, Strategy Unit) |
| Abstract: | This paper derives two mechanisms through which Bayesian-rational individuals with differing priors will tend to be relatively overconfident about their estimates and predictions, in the sense of overestimating the precision of these estimates. The intuition behind one mechanism is slightly ironic: in trying to update optimally, Bayesian agents overweight information of which they over-estimate the precision and underweight in the opposite case. This causes overall an over-estimation of the precision of the final estimate, which tends to increase as agents get more data. |
| Date: | 2010–11 |
| URL: | http://d.repec.org/n?u=RePEc:hbs:wpaper:11-049&r=gth |