Informational Smallness and the Scope for Limiting Information Rents

For an incomplete-information model of public-good provision with interim participation constraints, we show that e¢ cient outcomes can be approximated, with approximately full surplus extraction, when there are many agents and each agent is informationally small. The result holds even if agents' payoffs cannot be unambiguously inferred from their beliefs, i.e., even if the so-called BDP property ("Beliefs Determine Preferences") of Neeman (2004) does not hold. The contrary result of Neeman (2004) rests on an implicit uniformity requirement that is incompatible with the notion that agents are informationally small because there are many other agents who have information about them.surplus extraction, mechanism design, BDP, informational smallness, correlated information

Tenable threats when Nash Equilibrium is the norm

We formally assume that players in a game consider Nash Equilibrium (NE) the behavioral norm. In finite games of perfect information this leads to a refinement of NE: Faithful Nash Equilibrium (FNE). FNE is outcome equivalent to NE of the trimmed game, obtained by restricting the original tree to its NE paths. Thus, it always exists but it need not be unique. Iterating the norm ensures uniqueness of outcome. FNE may violate backward induction when subgame perfection requires play according to the SPE following a deviation from it. We thus provide an alternative view of tenable threats in equilibrium analysis

Allocative and Informational Externalities in Auctions and Related Mechanisms

We study the effects of allocative and informational externalities in (multi-object) auctions and related mechanisms. Such externalities naturally arise in models that embed auctions in larger economic contexts. In particular, they appear when there is downstream interaction among bidders after the auction has closed. The endogeneity of valuations is the main driving force behind many new, specific phenomena with allocative externalities: even in complete information settings, traditional auction formats need not be efficient, and they may give rise to multiple equilibria and strategic non-participation. But, in the absence of informational externalities, welfare maximization can be achieved by Vickrey-Clarke- Groves mechanisms. Welfare-maximizing Bayes-Nash implementation is, however, impossible in multi-object settings with informational externalities, unless the allocation problem is separable across objects (e.g. there are no allocative externalities nor complementarities) or signals are one-dimensional. Moreover, implementation of any choice function via ex-post equilibrium is generically impossible with informational externalities and multidimensional types. A theory of information constraints with multidimensional signals is rather complex, but indispensable for our study

Bounded Situation Calculus Action Theories

In this paper, we investigate bounded action theories in the situation calculus. A bounded action theory is one which entails that, in every situation, the number of object tuples in the extension of fluents is bounded by a given constant, although such extensions are in general different across the infinitely many situations. We argue that such theories are common in applications, either because facts do not persist indefinitely or because the agent eventually forgets some facts, as new ones are learnt. We discuss various classes of bounded action theories. Then we show that verification of a powerful first-order variant of the mu-calculus is decidable for such theories. Notably, this variant supports a controlled form of quantification across situations. We also show that through verification, we can actually check whether an arbitrary action theory maintains boundedness.Comment: 51 page

Essays in Game Theory.

I study how to model various strategic interactions with incomplete information and how to properly analyze them. The first chapter of the dissertation suggests new solution concepts for incomplete information games that are preceded by communication opportunities (communication games). Second chapter, written with Tilman Borgers, studies type spaces that model incomplete information among players with a specific property: the independence property. Third chapter suggests a new behavioral model to study real world decision makers' behavior. In the first chapter, I suggest new solution concepts for communication games to solve the following problem: traditional equilibrium analysis for communication games does not properly explain uncertainties about players' communication strategies, and so it excludes plausible outcomes of communication games from the set of equilibrium outcomes. Thus, I define correlated cheap talk equilibrium and correlated communication equilibrium. Epistemic analysis shows that new definitions represent the common knowledge of the Bayesian rationality of players with a common prior for a given communication game. In the second chapter, we study common prior type spaces in which for each agent the agent's payoff type and the agent's belief type are independent. Such type spaces deserve attention as the polar opposites of common prior type spaces in which agents' beliefs determine their preferences - a class of type spaces whose special properties are much studied. We find a necessary and sufficient condition for the independence of each agent's payoff type and belief type. Different agents' payoff types must be independent. Agents may hold payoff irrelevant information that must be jointly independent of all agents' payoff types. In the third chapter, I suggest a modified cognitive hierarchy (CH) model. Players have cognitive types which characterize their iterative reasoning abilities. Players know the existence of higher type players. In order to estimate higher type players' choices, players use other players' past choice data. Players improve their estimation with more information. The new model improves the original CH model by Camerer, Ho and Chong (2004), the replicator dynamics, and the fictitious play in explaining experimental results of the repeated beauty contest game and explaining the repeated market entry game.PhDEconomicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133277/1/otj_1.pd