APPROXIMATION MECHANISMS AND CHARACTERIZATION OF IMPLEMENTABLE SOCIAL CHOICE RULES

Abstract: The emerging field of Algorithmic Mechanism Design studies strategic implementations of social-choice functions that arise in computational settings -- most importantly, various resource allocation rules. The clash between computational constraints and incentive constraints is at the heart of this field. This happens whenever one wishes to implement a computationally-hard social choice function ( e.g. an allocation rule). In such cases, approximations or heuristics are computationally required, but it is not at all clear whether these can be strategically implemented.

MIXED BUNDLING AUCTIONS

Abstract: We study multi-object auctions where agents have multi-dimensional, private and additive valuations for heterogeneous objects. The revenue-maximizing auction for such environments is not known. I will first explain the relevant economic ideas / relations to monopoly pricing, and then the technical difficulties appearing in the auction context.  I will then focus on the revenue properties of a class of dominant strategy mechanisms where a weight is assigned to each partition of objects. The weights influence the probability with which partitions are chosen in the mechanism.

COUNTERFACTUALS

In this talk I will survey my account of counterfactuals. It consists of probabilistic conditions, backed up by causal conditions, themselves probabilistic (although such causal conditions will not be unpacked probabilistically in this talk). It makes uses of a probabilistic notion of processes. It does not make any use of the standard notion of closer or closest possible world or world state, as in some main-stream conceptions of counterfactuals. The talk will be to a large extent informal, but it will exhibit the basis on which a formal theory can be established.

An Operational Measure of Riskiness (joint work with Dean P. Foster)

AbstractWe define the riskiness of a gamble g as that unique number R(g) such that no-bankruptcy is guaranteed if and only if one never accepts gambles whose riskiness exceeds the current wealth.Paper: http://www.ma.huji.ac.il/hart/abs/risk.html   

Social Choice: Information, Power, Collective Rationality, Indeterminacy and Chaos

We will consider social welfare functions (SWFs) for N individuals(voters) and M alternatives. Those are functions which associate to every rofiles of individual order preference-relations on the alternatives, a social preference relation. We will discuss, power, aggregation of information, collective rationality, indeterminacy and chaos in the context of social choice. For this we will consider several properties of social welfare functions and the connections between them. The first property is well known (Condorcet and Arrow).

Rationality of Purity and Danger

Abstract: Mary Douglas, who has died recently, developed her Group / Grid theory based upon her field reseach in West Africa and a deep study of the Old Testament. The gist of her argument: Rationality is not universal, it is culture-dependent. And Culture, understood here as a way-of-life or a sort of Habitus, is a mix of values, behaviour and patterns of organisaion. Culture is shaped by 2 forces, Group and Grid. I intend to elaborate an these, and show how fruitful the theory has been in various empirical fields.

EFFICIENT, STRATEGY-PROOF AND ALMOST BUDGET-BALANCED ASSIGNMENT

Abstract Call a Vickrey-Clarke-Groves (VCG) mechanism to assign p identical objects among n agents, feasible if cash transfers yield no deficit. The efficiency loss of such a mechanism is the worst (largest) ratio of the budget surplus to the efficient surplus, over all profiles of non negative valuations. The optimal (smallest) efficiency loss

PURE SECRET CORRELATION AND FINITE AUTOMATA (JOINT WORK WITH OLIVIER GOSSNER)

AbstractIn this paper we study the conditions in which a team guarantees a successful coordination against a similar opponent. We consider a dynamical situation of a 3-players game in which each player is iden- tied by his ability to implement strategies. If the team payo is the opposite to its opponent one, the optimal coordination is character- ized by the value in correlated strategies of the zero-sum game. The ability of each player i is related to the number of states of thesmall-est machine which implements a strategy of player i, i.e.: mi.

EVOLUTION AND REPEATED GAMES (JOINT WORK WITH D. FUNDERBERG)

Abstract:We characterize the set of payoffs that are evolutionarily stable in two-player, symmetric repeated games when there is a small but positive probability that a player will make a mistake and a small but positive discount rate.

UNCOUPLED AUTOMATA AND PURE NASH EQUILIBRIA

Abstract: We study the problem of reaching a pure Nash equilibrium in multi-person games that are repeatedly played, under the assumption of uncoupledness: every player knows only his own payoff function.We consider strategies that can be implemented by finite-state automata, and characterize the minimal number of states needed in order to guarantee that a pure Nash equilibrium is reached in every game where such an equilibrium exists.

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