
on Microeconomics 
By:  Dirk Bergemann (Cowles Foundation, Yale University); Stephen Morris (Dept. of Economics, Princeton University) 
Abstract:  We define a notion of correlated equilibrium for games with incomplete information in a general setting with finite players, finite actions, and finite states, which we call Bayes correlated equilibrium. The set of Bayes correlated equilibria of a fixed incomplete information game equals the set of probability distributions over actions, states and types that might arise in any Bayes Nash equilibrium where players observed additional information. We show that more information always shrinks the set of Bayes correlated equilibria. 
Keywords:  Correlated equilibrium, Incomplete information, Robust predictions, Information structure 
JEL:  C72 D82 D83 
Date:  2011–10 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:1822&r=mic 
By:  Chiu Yu Ko (Boston College) 
Abstract:  This paper extends Bernheim and Whinston's (1986) menu auction model under transferable utilities to a framework with nontransferable utilities and budget constraints. Under appropriate definitions of equilibria, it is shown that every truthful Nash equilibrium (TNE) is a coalitionproof Nash equilibrium (CPNE) and that the set of TNE payoffs and the set of CPNE payoffs are equivalent, as in a transferable utility framework. The existence of a CPNE is assured in contrast with the possible nonexistence of Nash equilibrium under the definition by Dixit, Grossman, and Helpman (1997). Moreover, the set of CPNE payoffs is equivalent to the bidderoptimal weak core. 
Keywords:  nontransferable utility, menu auction, coalitionproof Nash equilibrium, truthful Nash equilibrium 
JEL:  C72 D79 
Date:  2011–10–20 
URL:  http://d.repec.org/n?u=RePEc:boc:bocoec:787&r=mic 
By:  Kieron Meagher 
Abstract:  In Hotelling style duopoly location games the product variety (or firm locations) is typically not socially optimal. This occurs because the competitive outcome is driven by the density of consumers at the margin while the socially optimal outcome depends on the whole distribution of consumer locations/tastes. We consider a natural extension of the standard model in which firms are imperfectly informed about the distribution of consumers, in particular firms are uncertain about the consumer mean. In the uniform case, as the aggregate uncertainty about the mean becomes large relative to the dispersion of consumers about the mean, competitive locations become socially optimal. A limit result on prices for discontinuous, logconcave densities shows the result will hold in a range of cases. 
JEL:  C72 D43 D81 L10 L13 R30 R39 
Date:  2011–10 
URL:  http://d.repec.org/n?u=RePEc:acb:cbeeco:2011555&r=mic 
By:  Pintér, Miklós; Udvari, Zsolt 
Abstract:  Ordinary type spaces (Heifetz and Samet, 1998) are essential ingredients of incomplete information games. With ordinary type spaces one can grab the notions of beliefs, belief hierarchies and common prior etc. However, ordinary type spaces cannot handle the notions of finite belief hierarchy and unawareness among others. In this paper we consider a generalization of ordinary type spaces, and introduce the so called generalized type spaces which can grab all notions ordinary type spaces can and more, finite belief hierarchies and unawareness among others. We also demonstrate that the universal generalized type space exists. 
Keywords:  type space; unawareness; finite belief hierarchy; generalized type space; generalized belief hierarchy; incomplete information games 
JEL:  D83 C72 
Date:  2011 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:34107&r=mic 
By:  Pintér, Miklós 
Abstract:  The notion of common prior is wellunderstood and widelyused in the incomplete information games literature. For ordinary type spaces the common prior is defined. Pinter and Udvari (2011) introduce the notion of generalized type space. Generalized type spaces are models for various bonded rationality issues, for finite belief hierarchies, unawareness among others. In this paper we define the notion of common prior for generalized types spaces. Our results are as follows: the generalization (1) suggests a new form of common prior for ordinary type spaces, (2) shows some quantum game theoretic results (Brandenburger and La Mura, 2011) in new light. 
Keywords:  Type spaces; Generalized type spaces; Common prior; Harsányi Doctrine; Quantum games 
JEL:  D83 C72 
Date:  2011 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:34118&r=mic 
By:  Thomas, C.D. 
Abstract:  In this thesis we present a new take on two classic problems of game theory: the "multiarmed bandit" problem of dynamic learning, and the "Colonel Blotto" game, a multidi mensional contest. In Chapters 24 we treat the questions of experimentation with congestion: how do players search and learn about options when they are competing for access with other players? We consider a bandit model in which two players choose between learning about the quality of a risky option (modelled as a Poisson process with unknown arrival rate), and competing for the use of a single shared safe option that can only be used by one agent at the time. We present the equilibria of the game when switching to the safe option is irrevocable, and when it is not. We show that the equilibrium is always inefficient: it involves too little experimentation when compared to the planner solution. The striking equilibrium dynamics of the game with revocable exit are driven by a strategic optionvalue arising purely from competition between the players. This constitutes a new result in the bandit literature. Finally we present extensions to the model. In particular we assume that players do not observe the result of their opponent's experimentation. In Chapter 5 we turn to the ndimensional Blotto game and allow battlefields to have different values. We describe a geometrical method for constructing equilibrium distribution in the Colonel Blotto game with asymmetric battlfield values. It generalises the 3dimensional construction method first described by Gross and Wagner (1950). The proposed method does particularly well in instances of the Colonel Blotto game in which the battlefield weights satisfy some clearly defined regularity conditions. The chapter also explores the parallel between these conditions and the integer partitioning problem in combinatorial optimisation. 
Date:  2011–08–28 
URL:  http://d.repec.org/n?u=RePEc:ner:ucllon:http://discovery.ucl.ac.uk/1325637/&r=mic 
By:  Bosi, Gianni; Zuanon, Magalì 
Abstract:  We characterize weak continuity of an interval order on a topological space by using the concept of a scale in a topological space. 
Keywords:  Weakly continuous interval order; continuous numerical representation 
JEL:  D00 C60 
Date:  2011–10–17 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:34182&r=mic 
By:  Barbanel, Julius B.; Brams, Steven J. 
Abstract:  A cake is a metaphor for a heterogeneous, divisible good. When two players divide such a good, there is always a perfect division—one that is efficient (Paretooptimal), envyfree, and equitable—which can be effected with a finite number of cuts under certain mild conditions; this is not always the case when there are more than two players (Brams, Jones, and Klamler, 2011b). We not only establish the existence of such a division but also provide an algorithm for determining where and how many cuts must be made, relating it to an algorithm, “Adjusted Winner” (Brams and Taylor, 1996, 1999), that yields a perfect division of multiple homogenous goods. 
Keywords:  Cakecutting; fair division; envyfreeness; adjusted winner; heterogeneous good 
JEL:  D63 D30 D74 C61 D61 C72 
Date:  2011–10–22 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:34263&r=mic 
By:  Brams, Steven J.; Jones, Michael A.; Klamler, Christian 
Abstract:  A cake is a metaphor for a heterogeneous, divisible good, such as land. A perfect division of cake is efficient (also called Paretooptimal), envyfree, and equitable. We give an example of a cake in which it is impossible to divide it among three players such that these three properties are satisfied, however many cuts are made. It turns out that two of the three properties can be satisfied by a 3cut and a 4cut division, which raises the question of whether the 3cut division, which is not efficient, or the 4cut division, which is not envyfree, is more desirable (a 2cut division can at best satisfy either envyfreeness or equitability but not both). We prove that no perfect division exists for an extension of the example for three or more players. 
Keywords:  Cakecutting; fair division; efficiency; envyfreeness; equitability; heterogeneous good 
JEL:  D71 D63 D30 D74 D61 C61 C72 
Date:  2011–10–22 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:34264&r=mic 