THE HOMER SIMPSON STUDENTS’ SEMINAR IN

GAME AND DECISION THEORY

 

The seminar includes talks given by research students in the fields of game and decision theory.  The aim of the seminar is to cover fundamental topics as well as current research.

All participants should promise to look interested, hint - not like this

    

 

Place: Schreiber building, Room 210   Time: Tuesdays 11:15-12:45.

 

To join or to leave the mailing list, please contact Roee Teper.

 

NEXT TALKS  

20.1.09        Ayala Arad,               The Tennis Coach Problem: A Game Theoretic and Experimental Study

Abstract: I will introduce a new allocation game called the Tennis Coach problem: Each tennis coach assigns his four different skilled players to four positions, and then each team plays all other teams in the tournament, where a player that was assigned by his coach to a particular position plays once against the player on the other team assigned to the same position. The game can be seen as an appealing modification of the popular colonel Blotto game (not as a special case), and it captures the essence of some interesting strategic interactions observed in competitive environments. The game is analyzed both theoretically and experimentally and serves as a platform for studying iterated reasoning and non-equilibrium models based on this concept.

PREVIOUS TALKS

13.1.09        Roee Teper,            Partially-Specified Probabilities (the notorious PSP)

Abstract: A Partially-Specified Probability is a list of random variables which their expectation are known (impressively simple, right?). Lehrer (2007) offers several models in decision and game theory, which are information (PSP) based. I will go through the motivation, give some examples and go over some of the results in his paper. 

30.12.08      Eilon Solan,               Bounded Memory Equilibrium      (to quote Eilon, "hot stuff") 

Abstract: We study two-player non-zero-sum infinitely repeated games in which the players are restricted to use strategies that are implementable by finite automata. Following Abreu and Rubisntein (1988), we assume that players have lexicographic utility: they would like to maximize their long-run average payoff, and, subject to that, they would like to minimize the size of their automaton.

We present a new solution concept, bounded memory equilibrium. Roughly, a pair of strategies is a bounded memory equilibrium if (1) if a player deviates to a smaller automaton, he loses, and (2) to profit, a player needs to deviate to an automaton which is "significantly larger" than his equilibrium automaton. We prove a folk theorem: every feasible and individually rational (relative to the min-max value in pure strategies) payoff vector is a bounded memory equilibrium.

23.12.08     Yoni Gur,              Quantum Probability and Likelihood Order of Nature States

Abstract: We will define a Quantum probability measure over a separable Hilbert space. We will define Likelihood

order over nature states in the meaning that A is more likely than B in the eyes of a decision maker if the decision

maker prefer betting that A occurs than betting that B occurs.  We will have a (breaf) discussion about when a

likelihood order that is defined over linear subspaces of a finite-dimentional Hilbert space, can be represented

by a quantum probability measure. We will discuss an axiomatic approach to the Quantic model, comparing the needed axioms

to the axioms used in the classic Savege model.  We will discuss the problem of characterizing such an order by behaviorally

justified axioms, while presenting an optional definition of acts, results and utility.

16.12.08     Assaf Cohen,        

Topic: Arbitrage Option Pricing

9.12.08      Shiri Alon Eron

Topic: Knightian decision making.

Abstract: A theory of choice under uncertainty is proposed which removes the completeness assumption from the Anscombe–Aumann formulation of Savage's theory and introduces an inertia assumption. The inertia assumption is that there is such a thing as the  status quo and an alternative is accepted only if it is preferred to the status quo. This theory is one way of giving rigorous expression to Frank Knight's distinction between risk and uncertainty.

 

18.11.08           Dotan Persitz

Topic:  Power in the Heterogeneous Connections Model: The Emergence of Core-Periphery Networks

Abstract: The heterogeneous connections model is a trivial generalization of the homogeneous connections model of Jackson and Wolinsky (1996) in which the intrinsic value of each connection is set by a discrete and symmetric function that depends solely on the types of the two agents that form the link. Core-periphery networks are defined as networks in which the agents' set can be partitioned into two subsets, one in which the members are completely connected among themselves and the other where there are no internal links. Using the intrinsic value function, a two-type society is defined as "power based" if both types of agents prefer to connect to one of the types (the "preferred") over the other (the "rejected"), controlling for path length. An exhaustive analysis shows that core-periphery networks, in which the "preferred" types are in the core and the "rejected" types are in the periphery, are crucial in the two-type "power based" society.  In particular, if the linking costs are not too low and not too high, at least one such network is pairwise stable. Moreover, in many cases these networks are the unique pairwise stable networks and in all cases they are the unique strongly efficient networks. The set of efficient networks often differs from the set of pairwise stable networks a discussion on this issue is developed. These results suggest heterogeneity accompanied by "power based" linking preferences as a natural explanation for many core-periphery structures observed in real life social networks

 

19.8.08            Yuval Heller

19.8.09             

I'll talk about two interesting results presented last July in  Chicago and Stony-Brook.

1) From the world congress in Chicago (Games 2008):
Kidney Exchange with Good Samaritan Donors: A Characterization
Tayfun Sonmez, M. Utku Unver

An applicative use of game theory in medicine. The authors analyze mechanisms to kidney exchange with good Samaritan donors where exchange is feasible not only among donor-patient pairs but also among such pairs and non-directed altruistic donors. We show that you request my donor-I get your turn mechanism is the only mechanism that is Pareto efficient, individually rational, strategy-proof, weakly neutral and consistent.

2) From the repeated games workshop at Stony-Brook:
Common Learning
MARTIN W. CRIPPS, JEFFREY C. ELY, GEORGE J. MAILATH, LARRY SAMUELSON (Econometrica 2008)
Consider two agents who learn the value of an unknown parameter by observing a sequence
of private signals. The signals are independent and identically distributed across
time but not necessarily across agents. The authors show that when each agent's signal space is
finite, the agents will commonly learn the value of the parameter, that is, that the true
value of the parameter will become approximate common knowledge. In contrast, if the
agents' observations come from a countably infinite signal space, common learning can fail.
 
 
8.7.08        Eilon Solan     

Topic:  Information Exchange in Games with Information Externalities

Abstract: I will discuss games with incomplete information and informational externalities, and provide a folk theorem. The talk will emphasize the nature of information exchange between the players.

 
1.7.08   Ayala Mashiah    

Topic:  General stopping games without simultaneous stopping

 

9.6.08        Shiri Alon     

Topic:  Purely Subjective Maxmin Expected Utility.

Abstract: The Maxmin Expected Utility decision rule represents choices made according to the minimal expectation with respect to a set of priors. Gilboa and Schmeidler axiomatized the maxmin decision rule in an environment where acts map states of nature into simple lotteries over a set of consequences. This paper presents axioms for a derivation of the maxmin decision rule in a purely subjective setting, where acts map states to points in a connected topological space. In such a setting one first constructs a (unique...) cardinal utility function that represents preferences over consequences (= constant acts). We did it using standard axioms, slightly weaker than what exists in the literature. This utility function can be used to represent preferences over all acts, because every act is equivalent to some constant act. The main innovation of our paper consists of the translation of uncertainty aversion and certainty independence axioms into the language of acts without any reference to mixtures of exogenously given lotteries. We avoid axioms of the form, "For any positive integer, n, and for any list of n acts...", or "... there exist a finite ...". Our new axioms are of the form: \for any k acts, . . . , if . . . , then . . . ", where k is less or equal to five.

 

3.6.08        Roee Teper    

Topic:  Uncertainty aversion and equilibrium existence in games with incomplete information.

Abstract:  Harsanyi (67-8) introduced the Bayes-Nash equilibrium in games with incomplete information, when players

are Bayesian expected-utility maximizers. We propose a new definition of equilibrium in such games, and show that under

some standard assumptions, equilibrium exist if and only if all players are averse to uncertainty.

 

29.4.08      Yaron Azrieli    

Topic:  Comparison of repeated experiments.

Abstract: In a seminal work, Blackwell (1953) characterized the case where one experiment (information structure) is better than another in any decision problem. Is it possible that there are two experiments, say I and I’, such that neither of them is better than the other but if we perform each of them twice then I is better than I’? I will show that the answer to this question is positive and give some examples that raise interesting open problems.

 
15.4.08      Doron Ravid     

Topic:  Prospect Theory: An Analysis of Decision under Risk (Kahneman and Tversky, Econometrica 1979).

Abstract: This paper presents a critique of expected utility theory as a descriptive model of decision making under risk, and develops an alternative model, called prospect theory. Choices among risky prospects exhibit several pervasive effects that are inconsistent with the basic tenets of utility theory. In particular, people underweight outcomes that are merely probable in comparison with outcomes that are obtained with certainty. This tendency, called the certainty effect, contributes to risk aversion in choices involving sure gains and to risk seeking in choices involving sure losses. In addition, people generally discard components that are shared by all prospects under consideration. This tendency, called the isolation effect, leads to inconsistent preferences when the same choice is presented in different forms. An alternative theory of choice is developed, in which value is assigned to gains and losses rather than to final assets and in which probabilities are replaced by decision weights. The value function is normally concave for gains, commonly convex for losses, and is generally steeper for losses than for gains. Decision weights are generally lower than the corresponding probabilities, except in the range of low probabilities. Overweighting of low probabilities may contribute to the attractiveness of both insurance and gambling.

 

26.2.08      Yuval Heller     

Topic:  A minority-proof cheap-talk protocol

Abstract: This paper analyzes the implementation of correlated equilibria that are immune to joint deviations of coalitions by cheap-talk protocols. We construct a universal cheap-talk protocol (a polite protocol that uses only 2-player private channels) that is resistant to deviations of fewer than half the players, and using it, we show that a large set of correlated equilibria can be implemented as Nash equilibria in the extended game with cheap-talk. Furthermore, we demonstrate that in general there is no cheap-talk protocol that is resistant for deviations of half the players.

The working paper can be downloaded from: http://www.tau.ac.il/~helleryu/minority.pdf

 

15.1.08      Nirit Agay    

Topic:  1. Ultimatum bargaining behavior of people affected by schizophrenia

2. Iowa Gambling Task

 

8.1.08        Shiri Alon-Eron     

Topic:  Expected utility without additivity

Abstract:  Decision making under uncertainty is often modelled as maximization of expected utility (EU). However, there are simple examples suggesting that such a description is not always suitable. I will present the famous Ellsberg paradox as such an example and discuss two generalizations of EU that settle this paradox. One is the nonadditive prior model of Schmeidler (1989) and the other is the multiple prior model of Gilboa and Schmeidler (1989).

 

25.12.07     Ayala Mashiah    

Topic:  Toward a Theory of Discounted Repeated Games with Imperfect Monitoring

Abstract:  The talk will survey a model of Abreu, Pearce and Stacchetti (1990) of repeated game with imperfect information. The model features unobservable actions, stochastic outcomes, and a publicly observable random variable correlated with players' private choices.

 

11.12.07     Assaf Cohen     

Topic: Decision-making under uncertainty: the Savage and Anscomb-Aumann models.

Abstract:  The talk will survey the classic models of Savage and Anscomb-Aumann of expected utility maximization in decision-making under uncertainty.

 

4.12.07      Yuval Heller     

Topic: Game-Theoretic Analysis of a Bankruptcy Problem from the Talmud

Abstract: For three different bankruptcy problems, the Mishna prescribes solutions which were for 2000 years unexplained, until in 1985, Aumann & Maschler in their classic paper "Game-Theoretic Analysis of a bankruptcy Problem from the  Talmud " (http://www.ma.huji.ac.il/raumann/pdf/45.pdf) show that the Mishna solution equal precisely to the nucleoli of the corresponding coalitional game. Following their paper, we will discuss in the lecture the Mishna problem and the related coalitional games concepts, and their rational, properties and justifications (in terms of modern game theory and in terms of old Talmudic principles).

 

20.11.07     Galit Ashkenazi 

Topic: The folk theorem in repeated games (cont.)

Abstract: I will discuss the folk theorem for finitely repeated games by Gossner.

 

13.11.07     Galit Ashkenazi 

Topic: The folk theorem in repeated games

Abstract: I shall shortly discuss the "classic" folk theorem, for infinitely repeated games and no discount, proved by Rubinstein (1994) and Aumann and Shapley (1994), and then I will discuss with more details the folk theorem for repeated games with discount (Fudenberg and Maskin 1986 & 1991).

 

30.10.07   Yaron Azrieli      

Topic: Equilibrium points of non-atomic games

Abstract: The talk will survey David Schmeidler’s paper (1973).   The main results are existence of equilibrium when there is a continuum of players endowed with a non-atomic measure and existence of pure equilibrium if payoffs depend only on aggregate behavior of opponents. If time permits we will also present two theorems of Aumann (1965) that are used in Schmeidler’s proof.