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on Game Theory |
| By: | Steven Landsburg (University of Rochester) |
| Abstract: | When the players in a game G can communicate with a referee via quantum technology (e.g. by sending emails composed on a quantum computer), their strategy sets naturally expand to include quantum superpositions of pure strategies. These superpositions lead to probability distributions among payoffs that would be impossible if players were restricted to classical mixed strategies. Thus the game G is replaced by a much larger “quantum game” GQ. When G is a 2 x 2 game, the strategy spaces of GQ are copies of the threedimensional sphere S3; therefore a mixed strategy is an arbitrary probability distribution on S3. These strategy spaces are so large that Nash equilibria can be difficult to compute or even to describe. The present paper largely overcomes this difficulty by classifying all mixed-strategy Nash equilibria in games of the form GQ. One result is that we can confine our attention to probability distributions supported on at most four points of S3; another is that these points must lie in one of several very restrictive geometric configurations. A stand-alone Appendix summarizes the relevant background from quantum mechanics and quantum game theory. |
| Date: | 2006–02 |
| URL: | http://d.repec.org/n?u=RePEc:roc:rocher:524&r=gth |
| By: | Ana B. Ania |
| Abstract: | Schaffer (1988) proposed a concept of evolutionary stability for finite-population models that has interesting implications in economic models of evolutionary learning, since it is related to perfectly competitive equilibrium. The present paper explores the relation of this concept to Nash equilibrium in particular classes of games, including constant-sum games, games with weak payoff externalities, and games where imitative decision rules are individually improving. An illustration of the latter is provided in the context of Bertrand oligopoly with homogeneous product which allows for a characterization of the set of evolutionarily stable prices. |
| JEL: | B52 C72 D43 D83 L13 |
| Date: | 2005–11 |
| URL: | http://d.repec.org/n?u=RePEc:vie:viennp:0601&r=gth |
| By: | Carsten Schmidt; Matthias Sutter; Werner Güth |
| Abstract: | In a large scale newspaper experiment 5,132 readers of the German weekly, Die Zeit, participated in a three-person bargaining game. In our data analysis we focus on (1) the influence of age, gender, profession and the medium chosen for participation on bargaining behavior and on (2) the external validity of student behavior (inside and outside the lab). We find that older participants and women care more about equal distributions and that Internet users are more self-regarding than those using mail or fax. Decisions made by students in the lab are rather similar to those made by students in the newspaper experiment. Furthermore, student behavior is not different from non-student behavior when the same age group is considered, indicating a high degree of external validity of student data. |
| Keywords: | ultimatum bargaining, newspaper experiment, Internet experiment |
| JEL: | C72 C93 D63 |
| Date: | 2005–12 |
| URL: | http://d.repec.org/n?u=RePEc:esi:discus:2006-04&r=gth |
| By: | Barry O'Neill (University of California, Los Angeles); Bezalel Peleg (Hebrew University of Jerusalem) |
| Abstract: | A two-house legislature can often be modelled as a proper simple game whose outcome depends on whether a coalition wins, blocks or loses in two smaller proper simple games. It is shown that there are exactly five ways to combine the smaller games into a larger one. This paper focuses on one of the rules, lexicographic composition, where a coalition wins G_1 => G_2 when it either wins in G_1, or blocks in G_1 and wins in G_2. It is the most decisive of the five. A lexicographically decomposable game is one that can be represented in this way using components whose player sets partition the whole set. Games with veto players are not decomposable, and anonymous games are decomposable if and only if they are decisive and have two or more players. If a player's benefit is assessed by any semi-value, then for two isomorphic games a player is better off from having a role in the first game than having the same role in the second. Lexicographic decomposability is sometimes compatible with equality of roles. A relaxation of it is suggested for its practical benefits. |
| Keywords: | simple games, voting, game composition, game decomposition, semi-value, decisiveness, fairness |
| JEL: | C71 D71 |
| Date: | 2006–02 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1559&r=gth |
| By: | Patrick Bajari; Han Hong |
| Abstract: | Recently, empirical industrial organization economists have proposed estimators for dynamic games of incomplete information. In these models, agents choose from a finite number actions and maximize expected discounted utility in a Markov perfect equilibrium. Previous econometric methods estimate the probability distribution of agents’ actions in a first stage. In a second step, a finite vector of parameters of the period return function are estimated. In this paper, we develop semiparametric estimators for dynamic games allowing for continuous state variables and a nonparametric first stage. The estimates of the structural parameters are T1/2 consistent (where T is the sample size) and asymptotically normal even though the first stage is estimated nonparametrically. We also propose sufficient conditions for identification of the model. |
| JEL: | L0 L5 C1 |
| Date: | 2006–02 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberte:0320&r=gth |
| By: | Juan José Ganuza; José S. Penalva |
| Abstract: | This paper studies the relationship between the auctioneer’s provision of information and the level of competition in private value auctions. We use a general notion of informativeness which allows us to compare the efficient with the (privately) optimal amount of information provided by the auctioneer. We show that in the private value setting more information increases the efficiency of the allocation while it also increases informational rents so that it is not optimal for the auctioneer to provide the efficient level of information. We also show that as the number of participants in the auction increases both the efficient and the optimal level of information increase and both converge when the number of bidders goes to infinity. |
| Keywords: | Auctions, Competition, Private Values, Optimal and Efficient Provision of Information |
| JEL: | D44 D82 D83 |
| Date: | 2006–01 |
| URL: | http://d.repec.org/n?u=RePEc:upf:upfgen:937&r=gth |
| By: | António Caleiro (Department of Economics, University of Évora) |
| Abstract: | The paper offers an analysis of the issues related to the election dates synchronisation between two countries. The first purpose of the paper is to analyse the circumstances in which a government of a single country, considered to be a small economy, has incentives, or not, to synchronise the domestic election dates with the election dates (not necessarily determined in an endogenous way) of a country performing the role of an ‘anchor’, considered to be a big economy. To achieve this purpose, the paper uses an asymmetric version of MILLER and SALMON’s (1990) model in order to derive the optimal domestic electoral period length, which, in this sense, can be said to be endogenously determined. The second main purpose of the paper is to re-analyse the situation being studied by considering that the foreign government also determines its election dates in an optimal way, this leading to a differential game played by the two incumbents from which incentives to totally synchronise the election dates may result. The paper shows that the interests of both economies in what concerns the existing electoral period length in the other economy are not always compatible. |
| Keywords: | Differential Games, Electoral business cycles, Election dates, Mandates durations, Synchronisation of elections |
| JEL: | C73 E32 E61 F42 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:evo:wpecon:05_2006&r=gth |
| By: | Shorish, Jamsheed (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria) |
| Abstract: | The rational expectations equilibrium has been criticized as an equilibrium concept in market game environments. Such an equilibrium may not exist generically, or it may introduce unrealistic assumptions about an economic agent's knowledge or computational ability. We define a rational expectations equilibrium as a probability measure over uncertain states of nature which exploits all available information in a market game, and which exists for almost all economies. Furthermore, if retrading is allowed, it is possible for agents to compute such a 'functional rational expectations equilibrium' using straightforward numerical fixed point algorithms. |
| Keywords: | Market game, Rational expectations equilibrium, Bayesian updating, Learning, Computation |
| JEL: | G12 D83 C63 |
| Date: | 2006–02 |
| URL: | http://d.repec.org/n?u=RePEc:ihs:ihsesp:186&r=gth |
| By: | Sjaak Hurkens; Nir Vulkan |
| Abstract: | We consider a dynamic model where traders in each period are matched randomly into pairs who then bargain about the division of a fixed surplus. When agreement is reached the traders leave the market. Traders who do not come to an agreement return next period in which they will be matched again, as long as their deadline has not expired yet. New traders enter exogenously in each period. We assume that traders within a pair know each other's deadline. We define and characterize the stationary equilibrium configurations. Traders with longer deadlines fare better than traders with short deadlines. It is shown that the heterogeneity of deadlines may cause delay. It is then shown that a centralized mechanism that controls the matching protocol, but does not interfere with the bargaining, eliminates all delay. Even though this efficient centralized mechanism is not as good for traders with long deadlines, it is shown that in a model where all traders can choose which mechanism to |
| Keywords: | Bargaining, Deadlines, Markets |
| JEL: | C73 C78 |
| Date: | 2006–02–01 |
| URL: | http://d.repec.org/n?u=RePEc:aub:autbar:660.06&r=gth |
| By: | Patrick Bajari; Han Hong; John Krainer; Denis Nekipelov |
| Abstract: | We propose a method for estimating static games of incomplete information. A static game is a generalization of a discrete choice model, such as a multinomial logit or probit, which allows the actions of a group of agents to be interdependent. Unlike most earlier work, the method we propose is semiparametric and does not require the covariates to lie in a discrete set. While the estimator we propose is quite flexible, we demonstrate that in most cases it can be easily implemented using standard statistical packages such as STATA. We also propose an algorithm for simulating the model which finds all equilibria to the game. As an application of our estimator, we study recommendations for high technology stocks between 1998-2003. We find that strategic motives, typically ignored in the empirical literature, appear to be an important consideration in the recommendations submitted by equity analysts. |
| JEL: | L0 L5 C1 |
| Date: | 2006–02 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:12013&r=gth |
| By: | Barry O'Neill (University of California, Los Angeles) |
| Abstract: | Leaders and historians see prestige as important, but international relations theorists have neglected the concept, in part for lack of a clear definition. It is proposed that a party "holds prestige" when group members generally believe that they generally believe that the party has a certain desirable quality, and this situation gives the party perceived power in the group. The definition gains support from a survey of international affairs writings on the sources of prestige. Prestige is strategically important when a party wants support from others who would rather join the side that more of the others are joining. Some general ways of acquiring prestige are discussed. Compared to achieving social progress, building and testing nuclear weapons is better at bearing prestige because it has distinct borders separating success and failure, because it is salient and because it involves the symbolism of power. In some cases when prestige is a factor, one can better demonstrate one’s ability to perform an accomplishment by refraining from doing it. The analysis yields suggestions for reducing nuclear proliferation. |
| Keywords: | prestige, nuclear weapons, common knowledge, signaling, countersignaling, global games, symbolism |
| JEL: | C72 D82 H56 |
| Date: | 2006–02 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1560&r=gth |