textThis thesis studies various computational and game-theoretic approaches to economic modeling. Unlike traditional approaches to economic modeling, the approaches studied in this thesis do not rely on the assumption that economic agents behave in a fully rational way. Instead, economic agents are assumed to be boundedly rational. Abandoning the assumption of full rationality has a number of consequences for the way in which economic reality is being modeled. Traditionally, economic models are mostly of a static nature and have a strong focus on deriving equilibria. Also, models are usually analyzed mathematically. In models of boundedly rational behavior, dynamic elements play a much more prominent role and there is less emphasis on equilibrium behavior. Also, to analyze models of boundedly rational behavior, researchers not only use mathematical techniques but they also rely heavily on computer simulations.

This thesis presents four studies into the modeling of boundedly rational behavior of economic agents. Two studies are concerned with investigating the emergence of cooperation among boundedly rational agents. One study focuses on cooperation among firms in a Cournot oligopoly market, while the other study examines cooperation in a spatial model of price-competing firms. The other two studies in this thesis are concerned with methodological issues in the use of evolutionary algorithms for economic modeling purposes. One study shows how evolutionary algorithms can be analyzed mathematically rather than using computer simulations. The other study criticizes the use of a so-called binary encoding in evolutionary algorithms.

https://repub.eur.nl/pub/26564/EPS2011248LIS9789058922922.pdf

Computational and Game-Theoretic Approaches for Modeling Bounded Rationality

Fingerprinting is a technique for generating a representation-independent functional signature for a game playing agent. Fingerprints can be used to compare agents across representations in an automatic fashion. The theory of fingerprints is developed for software agents that play the iterated prisoner's dilemma. Examples of the technique for computing fingerprints are given. This paper summarizes past results and introduces the following new results. Fingerprints of prisoner's dilemma strategies that are represented as finite-state machines must be rational functions. An example of a strategy that does not have a finite-state representation and which does not have a rational fingerprint function is given: the majority strategy. It is shown that the AllD- and AllC-based fingerprints can be derived from the tit-for-tat fingerprint by a simple substitution. Fingerprints for four new probe strategies are introduced, generalizing previous work in which tit-for-tat is the sole probe strategy. A trial comparison is made of evolved prisoner's dilemma strategies across three representations: finite-state machines, feedforward neural nets, and lookup tables. Fingerprinting demonstrates that all three representations sample the strategy space in a radically different manner, even though the neural net's and lookup table's parameters are alternate encodings of the same strategy space. This space of strategies is also a subset of those encoded by the finite-state representation. Shortcomings of the fingerprint technique are outlined, with illustrative examples, and possible paths to overcome these shortcomings are given.

/pdf/fingerprinting-visualization-and-automatic-analysis-of-3uj1jredmc.pdf

Fingerprinting: Visualization and Automatic Analysis of Prisoner's Dilemma Strategies

https://comunidad.udistrital.edu.co/malzate/files/2011/12/AGameTheoreticTrustModelOfCooperation.pdf

A game theoretic trust model for on-line distributed evolution of cooperation inMANETs

Mechanisms promoting the evolution of cooperation in two players and two strategies (22) evolutionary games have been investigated in great detail over the past decades. Understanding the effects of repeated interactions in multiplayer spatial games, however, is a formidable challenge. In this paper, we present a multiplayer evolutionary game model in which agents play iterative games in spatial populations. -player versions of the well-known Prisoner's Dilemma and the Snowdrift games are used as the basis of the investigation. These games were chosen as they have emerged as the most promising mathematical metaphors for studying cooperative phenomena. Here, we have adopted an experimental approach to study the emergent behavior, exploring different parameter configurations via numerical simulations. Key model parameters include the cost-to-benefit ratio, the size of groups, the number of repeated encounters, and the interaction topology. Our simulation results reveal that, while the introduction of iterated interactions does promote higher levels of cooperative behavior across a wide range of parameter settings, the cost-to-benefit ratio and group size are important factors in determining the appropriate length of beneficial repeated interactions. In particular, increasing the number of iterated interactions may have a detrimental effect when the cost-to-benefit ratio and group size are small.

Effects of Iterated Interactions in Multiplayer Spatial Evolutionary Games

The iterated prisoner's dilemma is an ideal model for the evolution of cooperation among payoff-maximizing individuals. It has attracted wide interest in the development of novel strategies since the success of tit-for-tat in Axelrod's iterated prisoner's dilemma competitions. Every strategy for iterated prisoner's dilemma utilizes a certain length of historical interactions with the opponent, which is regarded as the size of the memory, in making its choices. Intuitively, longer memory strategies must have an advantage over shorter memory strategies. In practice, however, most of the well known strategies are short memory strategies that utilize only the recent history of previous interactions. In this paper, the effect of the memory size of strategies on their evolutionary stability in both infinite length and indefinite length ${n}$ -person iterated prisoner's dilemma is studied. Based on the concept of a counter strategy, we develop a theoretical methodology for evaluating the evolutionary stability of strategies and prove that longer memory strategies outperform shorter memory strategies statistically in the sense of evolutionary stability. We also give an example of a memory-two strategy to show how the theoretical study of evolutionary stability assists in developing novel strategies.

/pdf/the-effect-of-memory-size-on-the-evolutionary-stability-of-cyhg93vr5i.pdf

The Effect of Memory Size on the Evolutionary Stability of Strategies in Iterated Prisoner's Dilemma

We discuss the evolution of strategies in a spatial iterated prisoner's dilemma (IPD) game in which each player is located in a cell of a two-dimensional grid-world. Following the concept of structured demes, two neighborhood structures are used. One is for the interaction among players through the IPD game. A player in each cell plays against its neighbors defined by this neighborhood structure. The other is for mating strategies by genetic operations. A new strategy for a player is generated by genetic operations from a pair of parent strings, which are selected from its neighboring cells defined by the second neighborhood structure. After examining the effect of the two neighborhood structures on the evolution of cooperative behavior with standard pairing in game-playing, we introduce a random pairing scheme in which each player plays against a different randomly chosen neighbor at every round (i.e., every iteration) of the game. Through computer simulations, we demonstrate that small neighborhood structures facilitate the evolution of cooperative behavior under random pairing in game-playing.

Evolution of iterated prisoner's dilemma game strategies in structured demes under random pairing in game playing

We discuss the evolution of cooperative behavior in the iterated prisoner's dilemma (IPD) game under random pairing in game playing. The main characteristic feature of this paper is the use of the random pairing scheme in which each player plays against a different randomly chosen opponent at every round of the dilemma game. Each player has a single-round memory strategy represented by a binary string of length five. The next action of a player is determined by its strategy based on the result of its previous round of the dilemma game. First we perform computational experiments to examine the evolution of cooperative behavior under the random pairing scheme using various parameter specifications. Experimental results show that the evolution of cooperative behavior is difficult independent of parameter specifications about the population size, the crossover probability, and the mutation probability. It is also shown that slightly better results (i.e., higher payoff) are obtained from smaller populations. Then we demonstrate the possibility of the evolution of cooperative behavior under the random matchmaking scheme in the case of a spatial IPD model where each player is located in a cell in a two-dimensional grid-world.

Evolution of cooperative behavior in the iterated prisoner's dilemma under random pairing in game playing

We examine the effect of spatial structures on the evolution of iterated prisoner’s dilemma (IPD) game strategies through computational experiments in single-dimensional and two-dimensional grid-worlds. Our computational experiments have two characteristic features. One is the use of a random pairing scheme in the IPD game where each player plays against a different randomly chosen opponent at every round of the dilemma game. The random pairing scheme makes it very difficult for players to evolve cooperative behavior. The other characteristic feature is the use of two neighborhood structures, which follows the concept of structured demes. One is for the interaction among players through the IPD game. A player in each cell in a grid-world plays against its neighbors defined by this neighborhood structure. The other is for the mating of strategies by genetic operations. A new strategy for a player is generated by genetic operations from a pair of parent strings, which are selected from its neighbors defined by the second neighborhood structure. It is shown that cooperative behavior is evolved only when the interaction neighborhood is very small and the mating neighborhood is small.

Effects of Spatial Structures on Evolution of Iterated Prisoner&#8217;s Dilemma Game Strategies in Single-Dimensional and Two-Dimensional Grids

In this paper we improve the performance of an evolutionary method for obtaining team strategies in a simulated robot soccer domain. In the previous method each team strategy was evaluated based on the goals and the goals against of a single game. It is possible for a good team strategy to be eliminated from the population in the evolutionary method as there is a high degree of uncertainty in the simulated soccer game. In order to tackle the problem of uncertainty, we propose a robust evaluation method using match history. The performance of team strategies in the proposed method is measured by the average goals and average goals against. Through a series of computational experiments, we show the effectiveness of our robust evaluation method.

Robust Evaluation of RoboCup Soccer Strategies by Using Match History

In this paper, we develop a goal keeper for simulated RoboCup soccer. The developed agent is an improved version of UvA Base team. We rst explain RoboCup and UvA Base team that is used as a base team. We also point out several flaws in the original keeper of the UvA Base team. Then, we describe how our keeper is developed. Finally, we show through computational experiments the effectiveness of the developed keeper.

N. Namikawa

Papers

Evolution of iterated prisoner's dilemma game strategies in structured demes under random pairing in game playing

Evolution of cooperative behavior in the iterated prisoner's dilemma under random pairing in game playing

Effects of Spatial Structures on Evolution of Iterated Prisoner’s Dilemma Game Strategies in Single-Dimensional and Two-Dimensional Grids

Robust Evaluation of RoboCup Soccer Strategies by Using Match History

Developing a Goal Keeper for Simulated RoboCup Soccer and its Performance Evaluation

N. Namikawa

Papers

Evolution of iterated prisoner's dilemma game strategies in structured demes under random pairing in game playing

Evolution of cooperative behavior in the iterated prisoner's dilemma under random pairing in game playing

Effects of Spatial Structures on Evolution of Iterated Prisoner&#8217;s Dilemma Game Strategies in Single-Dimensional and Two-Dimensional Grids

Robust Evaluation of RoboCup Soccer Strategies by Using Match History

Developing a Goal Keeper for Simulated RoboCup Soccer and its Performance Evaluation

Effects of Spatial Structures on Evolution of Iterated Prisoner’s Dilemma Game Strategies in Single-Dimensional and Two-Dimensional Grids