Experimental Investigation of a Cyclic Duopoly Game

The notion of a cyclic game has been introduced by Selten and Wooders (2001). They illustrate the concept by the analysis of a cyclic  duopoly game. The experiments reported concern this game. The game was played by eleven matching groups of six players each. The observed choice fre- quencies were compared with the predictions of Nash equilibrium, impulse balance equilibrium (Selten, Abbink and Cox (2005), Selten and Chmura (2007)) and two-sample equilbrium (Osborne and Rubinstein(1998)). Pair- wise comparisons by the Wilcoxon Signed-rank test show that impulse balance equilibrium as well as two-sample equilibrium have a significantly better predictive success than Nash equilibrium. The difference between impulse balance equilibrium and two-sample equilibrium is not   significant.In each matching group three players acted only in uneven periods and   the other three only in even periods. This game has two pure strategy equi- libria in which both types of players behave differently. The data exhibit a weak but significant tendency in the direction of coordination at a   pure strategy equilibrium.cyclic game duopoly experiment, impulse balance equilibrium, two-sample equilibrium

Learning in experimental 2×2 games

In this paper we introduce four new learning models: impulse balance learning, impulse matching learning, action-sampling learning, and payoff-sampling learning. With this models and together with the models of self- tuning EWA learning and reinforcement learning, we conduct simulations over 12 different 2×2 games and compare the results with experimental data obtained by Selten & Chmura (2008). Our results are two-fold: While the simulations, especially those with action-sampling learning and impulse matching learning successfully replicate the experimental data on the aggregate, they fail in describing the individual behavior. A simple inertia rule beats the learning models in describing individuals behavior.Learning, Action-sampling, Payo?-sampling, Impulse balance, Impulse matching, Reinforcement, self-tuning EWA, 2×2 games, Experimental data

How to Play 3x3 Games: A Strategy Method Experiment

Using the strategy method (Selten 1967) we elicit subjects' strategies for playing any 2-person 3x3-game with integer payoffs between 0 and 99.In each of 5 tournaments, every strategy pair plays 500000 games.The frequency of pure strategy equilibrium play increases from 51% in the first to 74% in the last tournament, with the equilibria that maximize joint payoff being preferred when multiple exist.For games without pure equilibria, strategies are typically based on elements of the best-reply cascade: MAP (maximize the expected payoff against uniformly randomizing opponents), BR-MAP (best reply to MAP), and BR-BR-MAP (best reply to BR-MAP).game theory;experimental economics

Complete synchronization of chaotic atmospheric models by connecting only a subset of state space

Connected chaotic systems can, under some circumstances, synchronize their states with an exchange of matter and energy between the systems. This is the case for toy models like the Lorenz 63, and more complex models. In this study we perform synchronization experiments with two connected quasi-geostrophic (QG) models of the atmosphere with 1449 degrees of freedom. The purpose is to determine whether connecting only a subset of the model state space can still lead to complete synchronization (CS). In addition, we evaluated whether empirical orthogonal functions (EOF) form efficient basis functions for synchronization in order to limit the number of connections. In this paper, we show that only the intermediate spectral wavenumbers (5-12) need to be connected in order to achieve CS. In addition, the minimum connection timescale needed for CS is 7.3 days. Both the connection subset and the connection timescale, or strength, are consistent with the time and spatial scales of the baroclinic instabilities in the model. This is in line with the fact that the baroclinic instabilities are the largest source of divergence between the two connected models. Using the Lorenz 63 model, we show that EOFs are nearly optimal basis functions for synchronization. The QG model results show that the minimum number of EOFs that need to be connected for CS is a factor of three smaller than when connecting the original state variables

Complete synchronization of chaotic atmospheric models by connecting only a subset of state space

Connected chaotic systems can, under some circumstances, synchronize their states with an exchange of matter and energy between the systems. This is the case for toy models like the Lorenz 63, and more complex models. In this study we perform synchronization experiments with two connected quasi-geostrophic (QG) models of the atmosphere with 1449 degrees of freedom. The purpose is to determine whether connecting only a subset of the model state space can still lead to complete synchronization (CS). In addition, we evaluated whether empirical orthogonal functions (EOF) form efficient basis functions for synchronization in order to limit the number of connections. In this paper, we show that only the intermediate spectral wavenumbers (5–12) need to be connected in order to achieve CS. In addition, the minimum connection timescale needed for CS is 7.3 days. Both the connection subset and the connection timescale, or strength, are consistent with the time and spatial scales of the baroclinic instabilities in the model. This is in line with the fact that the baroclinic instabilities are the largest source of divergence between the two connected models. Using the Lorenz 63 model, we show that EOFs are nearly optimal basis functions for synchronization. The QG model results show that the minimum number of EOFs that need to be connected for CS is a factor of three smaller than when connecting the original state variables

Stationary concepts for experimental 2x2-games

Five stationary concepts for completely mixed 2 x 2-games are experimentally compared: Nash equilibrium, quantal response equilibrium, action-sampling equilibrium, payoff-sampling equilibrium (Martin J. Osborne and Ariel Rubinstein 1998), and impulse balance equilibrium. Experiments on 12 games, 6 constant sum games, and 6 nonconstant sum games were run with 12 independent subject groups for each constant sum game and 6 independent subject groups for each nonconstant sum game. Each independent subject group consisted of four players 1 and four players 2, interacting anonymously over 200 periods with random matching. The comparison of the five theories shows that the order of performance from best to worst is as follows: impulse balance equilibrium, payoff-sampling equilibrium, action-sampling equilibrium, quantal response equilibrium, Nash equilibrium