Man vs. Machine in Chess: An Account by a Computer Chess World Champion

Programming a computer to defeat the best human chess players is one of the classical problems of AI and computer science. Turing and Shannon laid out the foundations, and hundreds of researchers and mavericks put their best efforts into it. I will discuss the ups and downs of the challenge, David Levy's bet, Kasparov's matches against Deep Blue and Deep Junior, and the computer chess world championships.

The Talmud On Transitivity (joint work with Shlomo Naeh)

Transitivity is a fundamental axiom in Economics that appears in consumer theory, decision under uncertainty, and social choice theory.While the appeal of transitivity is obvious, observed choices sometimes contradict it.This paper shows that treatments of violations of transitivity already appear in the rabbinical literature, starting with the Mishnah and the Talmud (1st-5th c CE). This literature offers several solutionsthat are similar to those used in the modern economic literature, as well as some other solutions that may be adopted in modern situations.We analyze several examples.

Benefits of Matchmaking

In the modern society norms towards relationships have changed significantly. In the past, a relationship once formed was expected to last. Nowadays, getting out of a relationship is not restricted by norms.Our model shows how value and a role of matchmaking changed with the changes in society. Using examples of online dating sites, we show that by imposing high cost on participants a matchmaker can provide matches yielding higher expected payoff than the general market. This is true even when the matchmaker has no specific information about the individuals.

Why we view the brain as computer

Computational neuroscientists employ computer models and simulations in studying brain functions. But, in addition, they view the modeled nervous system itself as computing. What does it mean to say that the brain computes? And what is the utility of the 'brain-as-computer' assumption in studying brain functions? In previous work, I argue that the algorithmic conception of computation is not adequate to address these questions. Here I introduce and explicate an alternative, "analog", conception of computation. The term 'analog' does not mean continuous, non-discrete or non-digital.

Endogenous Market Power

In this paper we develop a framework to study thin markets, in which all traders, buyers and sellers are large, in the sense that they all have market power (also known as bilateral oligopoly). Unlike the standard IO models our framework does not a priori assume that some traders do or do not have market power because they are large or small. Here, market power arises endogenously for each trader from market clearing and optimization by all agents. This framework allows for multiple goods and heterogeneous traders.

An Evolutionary Foundation of Rational Choice (JOINT WORK WITH CHRISTOPH KUZMICS)

A choice rule maps subsets of available alternatives to subsets of chosen alternatives. It is strictly rational if it is induced by a strict order on the grand set of alternatives. We compare intergenerational learning processes based on the distribution of choice rules a generation experiments with.

Cognitive Resources: How Less Can Be More

Many models of rational inference view the mind as if it were a supernatural being possessing demonic powers of reason, boundless knowledge, and all of eternity for making decisions. In reality, humans act under limited time, knowledge, and computational power.Across various cognitive research programs, the premise that human information-processing capacity is limited often goes hand in hand with the belief that these limitations are nothing but a liability.They are suspected of being the culprit behind reasoning lapses and of barring us from achieving the feats of a supercomputer.

The Strategic Value of Recall

This work studies the value of two-person zero-sum repeated games in which at least one of the players is restricted to (mixtures of) bounded recall strategies. A (pure) k-recall strategy is a strategy that relies only on the last k periods of history. This work improves previous results [Lehrer 1988, Neyman-Okada 2005] on repeated games with bounded recall. We provide an explicit formula for the asymptotic value of the repeated game as a function of the stage game, the duration of the repeated game, and the recall of the agents.

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