Simple Coalitional Strategy Profiles in Repeated Games

This paper is a version of the discussion paper titled "Simple coalitional strategy profiles"

A Review on Repeated Games and Reputations with Incomplete Information

In this project we review the effects of reputation within the context of game theory. This is done through a study of two key papers. First, we examine a paper from Fudenberg and Levine: Reputation and Equilibrium Selection in Games with a Patient Player (1989). We add to this a review Gossner’s Simple Bounds on the Value of a Reputation (2011). We look specifically at scenarios in which a long-run player faces a series of short-run opponents, and how the former may develop a reputation. In turn, we show how reputation leads directly to both lower and upper bounds on the long-run player’s payoffs.

A Review on Repeated Games and Reputations with Incomplete Information

In this project we review the effects of reputation within the context of game theory. This is done through a study of two key papers. First, we examine a paper from Fudenberg and Levine: Reputation and Equilibrium Selection in Games with a Patient Player (1989). We add to this a review Gossner’s Simple Bounds on the Value of a Reputation (2011). We look specifically at scenarios in which a long-run player faces a series of short-run opponents, and how the former may develop a reputation. In turn, we show how reputation leads directly to both lower and upper bounds on the long-run player’s payoffs.

On Limits to the Use of Linear Markov Strategies in Common Property Natural Resource Games

We derive conditions that must be satisfied by the primitives of the problem in order for an equilibrium in linear Markov strategies to exist in some common property natural resource differential games. These conditions impose restrictions on the admissible form of the natural growth function, given a benefit function, or on the admissible form of the benefit function, given a natural growth function.

Strategic Behavior and Collusion: An Application to the Spanish Electricity Market

The paper has two major contributions to the theory of repeated games. First, we build a supergame oligopoly model where firms compete in supply functions, we show how collusion sustainability is affected by the presence of a convex cost function, the magnitude of both the slope of demand market, and the number of rivals. Then, we compare the results with those of the traditional Cournot reversion under the same structural characteristics. We find how depending on the number of firms and the slope of the linear demand, collusion sustainability is easier under supply function than under Cournot competition. The conclusions of the models are simulated with data from the Spanish wholesale electricity market to predict lower bounds of the discount factors.

Three essays on game theory and bargaining

A PhD Dissertation, presented as part of the requirements for the Degree of Doctor of Philosophy from the NOVA - School of Business and Economics

The Ghost in the Machine: Inferring Machine-Based Strategies from Observed Behavior

We introduce a procedure to infer the repeated-game strategies that generate actions in experimental choice data. We apply the technique to set of experiments where human subjects play a repeated Prisoner's Dilemma. The technique suggests that two types of strategies underly the data.

Cooperative of Noncooperative Behavior?

In an abstract two-agent model, we show that every deterministic joint choice function compatible with the hypothesis that agents act noncooperatively is also compatible with the hypothesis that they act cooperatively. the converse is false.

A comment on "Rational learning lead to nash equilibrium" by professors Ehud Kalai and Ehud Lehrer

Kalai and Lebrer (93a, b) have recently show that for the case of infinitely repeated games, a coordination assumption on beliefs and optimal strategies ensures convergence to Nash equilibrium. In this paper, we show that for the case of repeated games with long (but finite) horizon, their condition does not imply approximate Nash equilibrium play. Recently Kalai and Lehrer (93a, b) proved that a coordination assumption on beliefs and optimal strategies, ensures that pIayers of an infinitely repeated game eventually pIay 'E-close" to an E-Nash equilibrium. Their coordination assumption requires that if players believes that certain set of outcomes have positive probability then it must be the case that this set of outcomes have, in fact, positive probability. This coordination assumption is called absolute continuity. For the case of finitely repeated games, the absolute continuity assumption is a quite innocuous assumption that just ensures that pIayers' can revise their priors by Bayes' Law. However, for the case of infinitely repeated games, the absolute continuity assumption is a stronger requirement because it also refers to events that can never be observed in finite time.

Types of evolutionary stability and the problem of cooperation.

The evolutionary stability of cooperation is a problem of fundamental importance for the biological and social sciences. Different claims have been made about this issue: whereas Axelrod and Hamilton's [Axelrod, R. & Hamilton, W. (1981) Science 211, 1390-1398] widely recognized conclusion is that cooperative rules such as "tit for tat" are evolutionarily stable strategies in the iterated prisoner's dilemma (IPD), Boyd and Lorberbaum [Boyd, R. & Lorberbaum, J. (1987) Nature (London) 327, 58-59] have claimed that no pure strategy is evolutionarily stable in this game. Here we explain why these claims are not contradictory by showing in what sense strategies in the IPD can and cannot be stable and by creating a conceptual framework that yields the type of evolutionary stability attainable in the IPD and in repeated games in general. Having established the relevant concept of stability, we report theorems on some basic properties of strategies that are stable in this sense. We first show that the IPD has "too many" such strategies, so that being stable does not discriminate among behavioral rules. Stable strategies differ, however, on a property that is crucial for their evolutionary survival--the size of the invasion they can resist. This property can be interpreted as a strategy's evolutionary robustness. Conditionally cooperative strategies such as tit for tat are the most robust. Cooperative behavior supported by these strategies is the most robust evolutionary equilibrium: the easiest to attain, and the hardest to disrupt.

Accounting for risk aversion in repeated prisoners’ dilemma games: an experimental test

We apply experimental methods to study the role of risk aversion on players’ behavior in repeated prisoners’ dilemma games. Faced with quantitatively equal discount factors, the most risk-averse players will choose Nash strategies more often in the presence of uncertainty than when future profits are discounted in a deterministic way. Overall, we find that risk aversion relates negatively with the frequency of collusive outcomes.

Proximity-to-goal as a constraint on patterns of behaviour in attacker–defender dyads in team games

The aim of this study was to determine whether spatiotemporal interactions between footballers and the ball in 1 vs. 1 sub-phases are influenced by their proximity to the goal area. Twelve participants (age 15.3 ± 0.5 years) performed as attackers and defenders in 1 vs. 1 dyads across three field positions: (a) attacking the goal, (b) in midfield, and (c) advancing away from the goal area. In each position, the dribbler was required to move beyond an immediate defender with the ball towards the opposition goal. Interactions of attacker-defender dyads were filmed with player and ball displacement trajectories digitized using manual tracking software. One-way repeated measures analysis of variance was used to examine differences in mean defender-to-ball distance after this value had stabilized. Maximum attacker-to-ball distance was also compared as a function of proximity-to-goal. Significant differences were observed for defender-to-ball distance between locations (a) and (c) at the moment when the defender-to-ball distance had stabilized (a: 1.69 ± 0.64 m; c: 1.15 ± 0.59 m; P < 0.05). Findings indicate that proximity-to-goal influenced the performance of players, particularly when attacking or advancing away from goal areas, providing implications for training design in football. In this study, the task constraints of football revealed subtly different player interactions than observed in previous studies of dyadic systems in basketball and rugby union.

Energy expenditure in adolescents playing new generation computer games

Objective: To compare the energy expenditure of adolescents when playing sedentary and new generation active computer games.

Design: Cross sectional comparison of four computer games. Setting Research laboratories.

Participants: Six boys and five girls aged 13–15 years.

Procedure: Participants were fitted with a monitoring device validated to predict energy expenditure. They played four computer games for 15 minutes each. One of the games was sedentary (XBOX 360) and the other three were active (Wii Sports).

Main outcome measure: Predicted energy expenditure, compared using repeated measures analysis of variance.

Results: Mean (standard deviation) predicted energy expenditure when playing Wii Sports bowling (190.6 (22.2) kl/kg/min), tennis (202.5 (31.5) kl/kg/min), and boxing (198.1 (33.9) kl/kg/min) was significantly greater than when playing sedentary games (125.5 (13.7) kl/kg/min) (P<0.001). Predicted energy expenditure was at least 65.1 (95% confidence interval 47.3 to 82.9) kl/kg/min greater when playing active rather than sedentary games.

Conclusions: Playing new generation active computer games uses significantly more energy than playing sedentary computer games but not as much energy as playing the sport itself. The energy used when playing active Wii Sports games was not of high enough intensity to contribute towards the recommended daily amount of exercise in children.

Comparison of energy expenditure in adolescents when playing new generation and sedentary computer games: cross sectional study

Objective : To compare the energy expenditure of adolescents when playing sedentary and new generation active computer games.

Design : Cross sectional comparison of four computer games.

Setting : Research laboratories.

Participants : Six boys and five girls aged 13-15 years.

Procedure : Participants were fitted with a monitoring device validated to predict energy expenditure. They played four computer games for 15 minutes each. One of the games was sedentary (XBOX 360) and the other three were active (Wii Sports).

Main outcome measure : Predicted energy expenditure, compared using repeated measures analysis of variance.

Results : Mean (standard deviation) predicted energy expenditure when playing Wii Sports bowling (190.6 (22.2) kJ/kg/min), tennis (202.5 (31.5) kJ/kg/min), and boxing (198.1 (33.9) kJ/kg/min) was significantly greater than when playing sedentary games (125.5 (13.7) kJ/kg/min) (P<0.001). Predicted energy expenditure was at least 65.1 (95% confidence interval 47.3 to 82.9) kJ/kg/min greater when playing active rather than sedentary games.

Conclusions : Playing new generation active computer games uses significantly more energy than playing sedentary computer games but not as much energy as playing the sport itself. The energy used when playing active Wii Sports games was not of high enough intensity to contribute towards the recommended daily amount of exercise in children.

The relationship between repeated sprint ability and the aerobic and anaerobic energy systems

A large number of team games require participants to repeatedly produce maximal or near maximal sprints of short duration with brief recovery periods. The purpose of the present study was to determine the relationship between a repeated sprint ability (RSA) test that is specific to the energy demands of Australian Rules football (ARF), and the aerobic and anaerobic energy systems.