Invited Speakers

Invited Speaker

Talk

Roko Aliprantis

Purdue University

aliprantismgmt.purdue.edu

Some applications of Riesz spaces to Economics, Finance, and Econometrics 

The mathematical theory of Riesz spaces (vector lattices) has been found to be very useful in many applied problems and optimization theory. In this general talk, we shall present several applications of Riesz spaces to economics, finance, and econometrics. The emphasis will be on the role of the lattice properties of Riesz spaces in these areas.

Robert Aumann

Hebrew University of Jerusalem

raumannmath.huji.ac.il

Assessing Strategic Risk  [PDF]

- joint work with Jacques H. Dreze

In recent decades, the concept of subjective probability has been increasingly applied to an adversary's choices in strategic games. A careful examination reveals that the standard construction of subjective probabilities does not apply in this context. We show how the difficulty may be overcome by means of a different construction.

Steven Brams

New York University

steven.bramsnyu.edu

A Minimax Procedure for Electing Committees  [PDF]

- joint work with D. Marc Kilgour and M. Remzi Sanver

A procedure for electing committees, called the minimax procedure, is described. While based on approval voting (AV), it chooses the committee that minimizes the maximum "Hamming distance" to all voters (minimax outcome). Such an outcome may be diametrically opposed to the usual AV outcome, which minimizes the sum of the Hamming distances to all voters (minisum outcome). Computer simulation is used to determine how much, on average, minimax and minisum outcomes diverge. The manipulability of the minimax procedure is also investigated.
The minimax procedure is applied to the 2003 Game Theory Society (GTS) election of a council of 12 new members from a list of 24 candidates. The 9th and 10th biggest vote-getters would have been displaced by the 16th and 17th biggest vote-getters if the minimax procedure had been used; there would have been more substantial differences if the size of the council had been made endogenous rather than being fixed at 12. It is argued that when few if any voters cast identical AV ballots, as was true in the GTS election (there were 2^24 = 16.8 million possible ballots), a minimax committee will better represent the interests of all voters than a minisum committee.

Stefano Demichelis

University of Pavia

stefanodnetcomp.it

On some (mis)applications of topology to game theory 

The theory of nash equilibria is, formally, that of fixed points of continuous functions and correspondences, so it is not surprising that some properties of the latter are relevant to strategic behaviour. In my talk I will show how some elementary algebraic topological facts have can shed light on the relation between the different stability concepts, I shall also discuss more promising approaches to the analysis of strategic behaviour.

Daniel Diermeier

Northwestern University

d-diermeierkellogg.northwestern.edu

Political Constitutions 

The talk will discuss recent applications of non-cooperative game-theory and structural estimation techniques to study the design of political constitutions.

Peter Eso

Northwestern University

esokellogg.northwestern.edu

Information Disclosure in Auctions 

- joint work with Balazs Szentes

We analyze a situation where a monopolist is selling an indivisible good to risk neutral buyers who only have an estimate of their private valuations. The seller can release, without observing, certain additional signals, which affect the buyers’ valuations. Our main result is that in the expected revenue maximizing mechanism, the seller makes available all the information that she can, and her expected revenue is the same as it would be if she could observe the released signals. We also show that this mechanism can be implemented by what we call a “handicap auction” in interesting applications (including one where the additional signal resolves an additive risk in the buyers’ valuations). In the first round of this auction, each buyer picks a price premium from a menu published by the seller (a smaller premium costs more). Then the seller releases the additional signals. In the second round, the buyers compete in a second-price auction where the winner pays the sum of his premium and the second highest non-negative bid.

Arieh Gavious

University of Toronto

ariehgrotman.utoronto.ca

Asymptotic Analysis of Large Auctions  [PDF]

- joint work with Gadi Fibich and Aner Sela

We study private-value auctions with a large number of bidders. We first calculate asymptotic approximations of the equilibrium bids and the seller's revenue in first-price auctions, regardless of whether the bidders are symmetric or asymmetric, risk-neutral or risk averse. We then show that with n bidders, the effects of risk aversion and of asymmetry on the equilibrium bids and on the seller's revenue are only O(1/n^2). Furthermore, it is demonstrated that first-price auctions with asymmetric bidders or with risk averse bidders are O(1/n^2) revenue equivalent to large classes of standard auctions.

John Geanakoplos

Yale University

john.geanakoplosyale.edu

Incentives in Games of Status: 100,99,...,1 or A,B,C?  [PDF]

- joint work with Pradeep Dubey

We show that if students care primarily about their status (relative rank) in class, they are best motivated to work not by revealing their exact numerical exam scores (100,99,...,1), but instead by clumping them in broad categories (A,B,C). If their abilities are disparate, the optimal grading scheme awards fewer A's than there are alpha-quality students, creating small elites. If their abilities are common knowledge, then it is better to grade them on an absolute scale (100 to 90 is an A, etc.) rather than on a curve (top 15% is an A, etc.). We develop criteria for optimal grading schemes in terms of the stochastic dominance between student performances.

Olivier Gossner

CERAS

Olivier.Gossnermail.enpc.fr

Ability and Knowledge  [PDF]

Incentives to innovation activities are tied to the value of information. In general, private benefits and social benefits to more information are not equal. Arrow (1962) shows that the private value of invention can be lower than its social value, which results in underinvestment in innovation activities. Hirshleifer (1971) exhibits situations where private value of information is positive whereas social value is null, which can result in overivestment in research, as well as situations in which private value for information is negative.
In the game-theoretic literature, the value of information is studied in the framework of games with incomplete information. Decision problems, zero-sum games, and games with common interest are classes of games which exhibit some monotonicity of equibibrium payoffs with information, but no such monotonicity exists in general games.
In a game with incomplete information, more information to a player implies a broader strategy set for this player in the corresponding game in normal form, hence more knowledge implies more ability. We prove that, on the other hand, given two normal form games G and G' such that players in a subset J of the set of players possess more strategies in G' than in G, there exist two games with incomplete information with normal forms G and G' such that players in J are more informed in the second than in the first. More ability can then be rationalized by more knowledge, and the result thus establishes the formal equivalence between ability and knowledge.
Our result allows us to understand the value of information as value of more ability. This explains why the classes of games with positive value of information are the ones with positive value for a larger strategy set. Our result can also be used to construct games with negative value information as in Kamien, Tauman and Zamir (1990).

John Hillas

University of Auckland

j.hillasauckland.ac.nz

On the relation between backward and forward induction 

We consider the relation between forward and backward induction. An example shows that a strong relation, previously conjectured by one of the authors, is incorrect. Two weaker results, one restricting attention to two player games and one weakening the notion of forward induction, are shown.

Sergei Izmalkov

MIT

izmalkovMIT.EDU

Shill-bidding and optimal auctions 

A single object is for sale to N asymmetric buyers in the independent private values setting by means of an English auction. We consider implications of seller's active participation in the bidding process, or shill bidding. Our main result is that the English auction with shill bidding has an equilibrium that is outcome equivalent to the optimal mechanism of Myerson (1981). Thus, not only the optimal auction can be implemented by a detailed-free mechanism, this is done by the most common of auction forms.
Our second goal is to stress that the choice of the game to model a particular market interaction and the choice of the solution concept to it are joined. In particular, ability to commit by one of the players undermines dominant strategy or ex post equilibrium conditions. We propose an asymmetric equilibrium concept, a buyer's ex post equilibrium, and show how it can be effectively used to reduce common knowledge requirements for the optimal equilibrium to exist.

Ehud Kalai

Northwestern University

kalaikellogg.northwestern.edu

Extensive Robustness Revisited 

Being extensively robust means that an equilibrium of a simultaneous move game G survives even if the simultaneous move assumption is relaxed (e.g., it allows for variations in the order of moves, information leakage, revisions, commitments, control over opponents’ moves, cheap-talk announcements etc.). In a recent paper the author shows that the equilibria of games with many semi anonymous players are extensively robust.
Formally, an equilibrium is defined to be extensively robust if it survives in all extensive versions of the underlying game G. This paper introduces a simple yet very general notion of extensive version, and argues that large games are extensively robust even under this significantly stronger notion.

Vijay Krishna

Penn State University

vkrishnapsu.edu

Mechanism Design under Imperfect Commitment 

Mechanism design theory rests on the assumption that the designer can commit to---that is, contract on---the workings of the mechanism. In practice, the power or willingness to commit is rarely absolute and in its absence many insights of mechanism design theory are no longer valid. For instance, the celebrated revelation principle no longer holds. We investigate a model of optimal contracting between an uninformed principal and an informed agent where the principal's commitment power is imperfect---while the principal can contract on the agent's compensation, he is unable to, or unwilling to, contract on other decisions. As a first step, we establish a limited revelation principle that applies in this context . We then exhibit some features of the optimal contract---while full alignment of interests combined with delegation of authority is feasible, it is never optimal. The optimal contract is "bang-bang"---in one region of the state space, full alignment takes place, in the the other, no alignment takes place. These contracts are then to those in which the principal has full commitment power as well as to several "informal" institutional arrangements.

Michael Maschler

Hebrew University of Jerusalem

maschlervms.huji.ac.il

Applying the Reduced Game Property to Analyze Cores and Nucleoli of Various Enterprizes  [PDF]

Cooperative game theory faces two serious problem whenever there is a need to apply it:
(1) Quite often, beyond the general definition, one knows little about the solution and so finds it difficult to decide which solution to adopt.
(2) Even if one decides to employ a certain solution concept, one cannot compute it, because one cannot even load a computer with a worth function of a middle-sized game.
Research therefore is concentrated in studying family of games of specific nature with the hope of using their properties in order to find the structures of their solutions and in order to facilitate the computation of these solutions. One feature that can be of help is the reduced game property that states that if some of the players leave the game, leaving behind their payments, to help whoever needs them, then the rest of the players find themselves in the solution of their reduced game. This is in a sense a cooperative game theoretical analog of the Nash equilibrium notion of non-cooperative game. Applying the reduced game property has its own difficulties. One has to relate it to the real situation. Often, it does not belong to the class of games we started with and one has to extend the class. The study of the reduced game, although simpler than the study of the original problem, but it
is not obvious.
We shall illustrate theses ideas by a study of the Chinese postman problem — a study in which H. Hammers, D. Granot, J. Kuipers and me were involved, and pass to other examples in which the reduced game property was of prime importance.

Wojciech Olegewski

Northwestern University

wonorthwestern.edu

The Folk Theorem for All Games with Almost Perfect Monitoring 

- joint work with Johannes Horner

We study repeated games in which monitoring is private. We prove the folk theorem for all two-player games assuming that the monitoring is almost perfect, but not necessarily almost public.

Thomas Palfrey

CalTech

trphss.caltech.edu

Self-Correcting Information Cascades  [PDF]

- joint work with Jacob Goeree, Brian Rogers, and Richard McKelvey

In laboratory experiments, information cascades are ephemeral phenomena, collapsing soon after they form, and then
reforming again. These formation/collapse/reformation cycles occur frequently and repeatedly. Cascades may be reversed (collapse followed by a cascade on a different state) and more often than not, such a reversal is self-correcting: the cascade switches from the incorrect to the correct state. Past experimental work focused on relatively short horizons, where these interesting dynamics are rarely observed. We present experiments with a longer horizon, and also investigate the effect of signal informativeness. We propose a theoretical model, based on quantal response equilibrium, where temporary and self-correcting cascades arise as equilibrium phenomena. The model also predicts the systematic differences we observe experimentally in the dynamics, as a function of signal informativeness. We extend the basic model to include a parameter measuring base rate neglect and find it to be a statistically significant factor in the dynamics, resulting in somewhat faster rates of social learning.

Jerome Renault

CEREMADE, University Paris 9

renaultceremade.dauphine.fr

Multicast communication in networks: reliability and security of information transmission 

- joint work with T. Tomala

This work takes place in the general context of strategic transmission of information. We concentrate on a simple model of multicast communication, where the players are distant nodes in some network modelled by a graph, and player a (the sender) wants to send some information to player b (the receiver). The network is said to be T-reliable if no malevolent adversary controlling T nodes can prevent player a to send some information to player b. It is said to be T-secure if no malevolent adversary controlling T nodes can prevent player a to send privately some information to player b. Reliability and security are studied, and a few links with the existence of equilibria in repeated games with incomplete information, and with computer science problems are presented.

Andrew Schotter

New York University

andrew.schotternyu.edu

Talking Ourselves to Efficiency: Coordination in Inter-Generational Minimum Games with Private, Almost Common and Common Knowledge of Advice 

We present an inter-generational version of the Van Huyck et al.'s (1990) Minimum Game. 8 subjects play the game for 10 periods. Afterwards each participant is replaced by another agent, his laboratory descendent, who then plays the game for another 10 periods with a group of new subjects. The generations are non-overlapping. Advice from a member of one generation is passed along to his successor via free-form messages that generation t players leave for their generation t+1 successors. It was our conjecture that using such an inter-generational design subjects would be able to "talk themselves to efficiency" in the sense of converging to the payoff-dominant outcome. What we find is that there is a quality threshold with advice. If the advice offered to subjects is sufficiently strong in urging them to cooperate then as long as that advice is offered in a public manner (either as common knowledge or as what we call "almost common knowledge") we can expect cooperation to follow. However, if the advice quality is below a threshold then cooperation is likely to result only if the advice is not only public but also distributed in a manner that makes it common knowledge.

Lloyd Shapley

UCLA

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A Walrasian Core? 

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Sylvain Sorin

U. Pierre et Marie Curie

sorinmath.jussieu.fr

Differential inclusions, stochastic approximations and dynamics in games  [PDF]

- joint work with M. Benaim and J. Hofbauer

The dynamical systems approach to stochastic approximation is generalized to the case where the mean differential equation is replaced by a differential inclusion.
The limit set theorem of Benaim and Hirsch is extended to this situation. Internally chain transitive sets and attractors are studied in detail for set-valued dynamical systems. Applications to game theory are given, in particular to Blackwell's approachability theorem and the convergence of fictitious play.

William Sudderth

University of Minnesota

billstat.umn.edu

Strategic Market Games with Production  [PDF]

We consider several models of a simple economy in which a single nondurable good is produced and consumed in each of a countable number of time periods. The agents seek to maximize the expectation of their total discounted utility derived from consumption of the good.
In the simplest model a single agent in isolation produces for his or her own personal consumption. The agent must decide in each time period how much of the good to consume and how much to put into production for the future.
Another model has a continuum of producer-consumer agents who sell the goods they produce in a market and purchase goods in the same market for consumption and as input for further production. The agents hold money and are required to pay cash to purchase goods in the market. They may also be allowed to borrow money from ( or deposit money in) a central bank.
A third model has a continuum of agents who consume and a continuum of firms that produce. The firms sell the goods they produce in a market and seek to maximize profit. The firms are owned mutually by the agents and pay their profits to the agents each period as dividends.
All the models considered can be regarded as stochastic games and we look for a stationary equlibrium in each case. We can then compare the welfare of the agents in the strategic market games to that of the single agent in isolation.
Analytic solutions are available when there is no uncertainty in the production process. If production is subject to random shocks, such solutions are typically not possible.
This talk is based on joint work with John Geanakoplos, Ioannis Karatzas, and Martin Shubik.

Moshe Tennenholtz

Technion

moshetie.technion.ac.il

Computation Social Systems: Reputations Systems and Non-Coperative Computation 

The Internet exhibits forms of interactions which are not captured by existing models in economics, computer science, artificial intelligence and game theory. New models are needed in order to deal with these multi-agent interactions. In this talk we discuss two such models: reputation systems and non-cooperative computation. In reputation systems we are given a reputation graph, where the nodes are agents and the edges correspond to feedback by the agents on the importance/reliability of other agents. The objective is to rank the agents based on this information, in order to cature their importance or reaibility. An example is Google's page rank, where pages are ranked based on the Internet link structure. In the talk we will briefly present an axiomatic approach to the above problem. In non-cooperative computation the objective is to compute a function based on private information held by the agents (e.g. each agent may have a private bit of information: 0 or 1, and the objective is to compute the majority function). However, although agents may wish to compute the result of the function, they may have a secondary objective of misleading others, and (if access to infromation is costly) might free-ride on other agents' computations. In the talk we briefly discuss few results about which (and how) functions can be correctly computed taking such incentives into account. Together, the talk will expose the audience to several challenges for the theories of social choice and mechanism design, bridging some of the gap between computer science and game theory. The part of presentation dealing with non-cooperative computation is based on joint work with Yoav Shoham and Rann Smorodinsky

Nicolas Vieille

Université Montesquieu Bordeaux IV

vieillepoly.polytechnique.fr

Timing games with informational externalities  [PDF]

- joint work with Dinah Rosenberg (Paris 13) and Eilon Solan (Tel Aviv University and Northwestern University)

We analyze the following game of timing with incomplete information. At each stage n in N, each (of finitely many) player i has to choose whether to stay in or to drop out from the game. If she stays in, she receives a random payoff X_i^n. Once out, she receives 0 forever. The various payoffs X_i^n are conditionally independent given a state of nature £, selected at stage 0 according to some prior distribution.

A key feature of our game is the information structure. Payoffs are private information, while exit decisions are publicly observed. The interaction of the players is therefore of an informational nature: player i cares about player j's decisions, since these may reveal something about player j's private information on £.

This game relates to various strands of literature. From the viewpoint of social learning with endogenous timing (e.g., Chamley Gale (Econ, 1994)), the distinguishing feature of our game is that players keep receiving private signals as time proceeds. When compared with the strategic experimentation literature (e.g.,Bolton Harris (Econ, 1999)), our game is characterized by the fact that payoffs are not publicly observed, so that posterior beliefs are not common knowledge. On the other hand, our game can be viewed as a strategic version of real options problems (e.g., Dcamps, Mariotti,Villeneuve (2001)). Finally, it bears some relation to the multi-armed bandit problems studied in statistics (e.g. Ferguson (2004)).

Under minimal assumptions, we prove that all equilibria are in pure strategies and incorporate the public information (players' past decisions) in a particularly simple way. In addition, we provide a number of qualitative properties of these equilibria, and we fully describe the limit equilibrium, as the number of players increases to infinity. The intricacy of the posterior beliefs of different orders, makes it impossible to perform explicit computations.

Myrna Wooders

University of Warwick

M.Wooderswarwick.ac.uk

Behavioural Conformity and Purification in Games with Many Players  [PDF]

- joint work with Edward Cartwright and Reinhard Selden

This presentation, based on joint research with Edward Cartwright and, in part, with Reinhard Selten, addresses the question of whether behavioural conformity can be consistent with (approximate) Nash equilibrium in pure strategies in strategic games with many players. A major focus of the presentation will be purification results for incomplete information games with countable action sets and countable (Harsanyi) types and a new mathematical result underlying the game theoretic results. Finally, ex-post Nash equilibria are related to approximate Bayesian equilibria.

Muhamet Yildiz

MIT

myildizmit.edu

Finite-order implications of any equilibrium  [PDF]

- joint work with Jonathan Weinstein

Present economic theories make a common-knowledge assumption that implies that the first or the second-order beliefs determine all higher-order beliefs. We analyze the role of such closing assumptions at finite orders by instead allowing higher orders to vary arbitrarily. Assuming that the space of underlying uncertainty is sufficiently rich, we show that the resulting set of possible outcomes, under an arbitrary fixed equilibrium, must include all outcomes that survive iterated elimination of strategies that are never a strict best reply. For many games, this implies that, unless the game is dominance-solvable, every equilibrium will be highly sensitive to higher-order beliefs, and thus economic theories based on such equilibria may be misleading. Moreover, every equilibrium is discontinuous at each type for which two or more actions survive our elimination process.