The Minority of Three-Game: An Experimental and Theoretical Analysis

We report experimental and theoretical results on the minority of three-game where three players have to choose one of two alternatives independently and the most rewarding alternative is the one chosen by a single player. This coordination game has many asymmetric equilibria in pure strategies that are non strict and payoff-asymmetric, and a unique symmetric mixed strategy equilibrium in which each player's behavior is based on the toss of a fair coin. We show that such a straightforward behavior is predicted by Harsanyi and Selten's (1988) equilibrium selection theory as well as alternative solution concepts like impulse balance equilibrium and sampling equilibrium. Our results indicate that participants rely on various decision rules, and that only a quarter of them decide according to the toss of a fair coin. Reinforcement learning is the most successful decision rule as it describes best the behavior of about a third of our participants.Coordination, Minority game, Mixed strategy, Learning models, Experiments

Three Puzzles on Mathematics, Computation, and Games

In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear programming. The second puzzle is about errors made when votes are counted during elections. The third puzzle is: are quantum computers possible?Comment: ICM 2018 plenary lecture, Rio de Janeiro, 36 pages, 7 Figure

Deferred compensation and gift exchange: an experimental investigation into multi-period labor markets

This paper examines the relationship between firms’ wage offers and workers’ supply of effort using a three-period experiment. In equilibrium, firms will offer deferred compensation: first period productivity is positive and wages are zero, while third period productivity is zero and wages are positive. The experiment produces strong evidence that deferred compensation increases worker effort; in about 70 percent of cases subjects supplied the optimal effort given the wage offer, and there was a strong effort response to future-period wages. We also find some evidence of gift exchange; worker players increased the effort levels in response to above equilibrium wage offers by a human, but not in response to similar offers by a computer. Finally, we find that firm players who are initially hesitant to defer compensation learn over time that it is beneficial to do so

Pensions in the laboratory: the role of commitment and reputation for deferred compensation in multi-period labor contracts

This paper examines the relationship between firms‘ wage offers and workers‘ supply of effort in a multi-period environment. If firms are able to commit to a schedule of wage payments, in equilibrium they will offer deferred compensation: first-period productivity is positive and wages are zero, while last-period productivity is zero and wages are positive. Workers respond to deferred compensation by supplying sufficient effort to avoid dismissal. In the absence of commitment, firms pay zero wages and workers supply low effort. The experiment produces strong evidence of these predictions. With commitment, we frequently observe deferred compensation and relatively high worker effort. In the absence of commitment, we observe no deferred compensation, much lower wages, and little worker effort. A third treatment where commitment is not possible, but firms are able to build a reputation, produces an intermediate result. Finally, we also find some evidence of gift exchange, in particular in the absence of commitment when deferred compensation does not work

Progress in Behavioral Game Theory

Is game theory meant to describe actual choices by people and institutions or not? It is remarkable how much game theory has been done while largely ignoring this question. The seminal book by von Neumann and Morgenstern, The Theory of Games and Economic Behavior, was clearly about how rational players would play against others they knew were rational. In more recent work, game theorists are not always explicit about what they aim to describe or advise. At one extreme, highly mathematical analyses have proposed rationality requirements that people and firms are probably not smart enough to satisfy in everyday decisions. At the other extreme, adaptive and evolutionary approaches use very simple models-mostly developed to describe nonhuman animals-in which players may not realize they are playing a game at all. When game theory does aim to describe behavior, it often proceeds with a disturbingly low ratio of careful observation to theorizing

To Bat or Not to Bat: An Examination of Contest Rules in Day-night Limited Overs Cricket

The tradition of tossing a coin to decide who bats first in a cricket match introduces a randomly-assigned advantage to one team that is unique in sporting contests. In this paper we develop previous work on this issue by examining the impact of the toss on outcomes of day-night one day international games explicitly allowing for relative team quality. We estimate conditional logit models of outcomes using data from day-night internationals played between 1979 and 2005. Other things equal, we find that winning the toss and batting increases the probability of winning by 31%. In contrast, winning the toss does not appear to confer any advantage if the team choose to bowl first.cricket, contest rules, match results, competitive balance, outcome uncertainty

Parametrization of stochastic inputs using generative adversarial networks with application in geology

We investigate artificial neural networks as a parametrization tool for stochastic inputs in numerical simulations. We address parametrization from the point of view of emulating the data generating process, instead of explicitly constructing a parametric form to preserve predefined statistics of the data. This is done by training a neural network to generate samples from the data distribution using a recent deep learning technique called generative adversarial networks. By emulating the data generating process, the relevant statistics of the data are replicated. The method is assessed in subsurface flow problems, where effective parametrization of underground properties such as permeability is important due to the high dimensionality and presence of high spatial correlations. We experiment with realizations of binary channelized subsurface permeability and perform uncertainty quantification and parameter estimation. Results show that the parametrization using generative adversarial networks is very effective in preserving visual realism as well as high order statistics of the flow responses, while achieving a dimensionality reduction of two orders of magnitude

A simple questionnaire can change everything: Are strategy choices in coordination games stable?

This paper presents results from an experiment designed to study the effect of self reporting risk preferences on strategy choices made in a subsequently played 2x2 coordination game. The main finding is that the act of answering a questionnaire about one's own risk preferences significantly alters strategic behavior. Within a best response correspondence framework, this result can be explained by a change in either risk preferences or beliefs. We find that self reporting risk preferences induces an increase in subjects' risk aversion while keeping their beliefs unchanged. Our findings raise some questions about the stability of strategy choices in coordination games. --coordination game,questionnaire,risk preferences,beliefs,best response correspondence