Limits...
Learning with repeated-game strategies.

Ioannou CA, Romero J - Front Neurosci (2014)

Bottom Line: In the Prisoner's Dilemma game, we find that the strategy with the most occurrences is the "Grim-Trigger." In the Battle of the Sexes game, a cooperative pair that alternates between the two pure-strategy Nash equilibria emerges as the one with the most occurrences.In the Stag-Hunt and Chicken games, the "Win-Stay, Lose-Shift" and "Grim-Trigger" strategies are the ones with the most occurrences.Overall, the pairs that converged quickly ended up at the cooperative outcomes, whereas the ones that were extremely slow to reach convergence ended up at non-cooperative outcomes.

View Article: PubMed Central - PubMed

Affiliation: Department of Economics, University of Southampton Southampton, UK.

ABSTRACT
We use the self-tuning Experience Weighted Attraction model with repeated-game strategies as a computer testbed to examine the relative frequency, speed of convergence and progression of a set of repeated-game strategies in four symmetric 2 × 2 games: Prisoner's Dilemma, Battle of the Sexes, Stag-Hunt, and Chicken. In the Prisoner's Dilemma game, we find that the strategy with the most occurrences is the "Grim-Trigger." In the Battle of the Sexes game, a cooperative pair that alternates between the two pure-strategy Nash equilibria emerges as the one with the most occurrences. In the Stag-Hunt and Chicken games, the "Win-Stay, Lose-Shift" and "Grim-Trigger" strategies are the ones with the most occurrences. Overall, the pairs that converged quickly ended up at the cooperative outcomes, whereas the ones that were extremely slow to reach convergence ended up at non-cooperative outcomes.

No MeSH data available.


Related in: MedlinePlus

Battle of the sexes.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4115627&req=5

Figure 4: Battle of the sexes.

Mentions: The payoff matrix of the Battle of the Sexes game is indicated in Figure 1B. In this game, there are two pure-strategy equilibria: (A, B) and (B, A). Figure 4 shows the results of the simulations. In particular, Figure 4A shows the relative frequency of automaton pairs played over the last 1000 periods. The plot covers a large number of automata although Automaton 12 and Automaton 18 show up most frequently. Automaton 12 switches actions every period unless both players choose B in the previous period. Automaton 18 switches actions every period unless both players choose A in the previous period. Therefore, a pair consisting of Automaton 12 and Automaton 18 would end up alternating between the two pure-strategy Nash equilibria of the stage game. Each automaton would thus earn an average payoff of 3. This is shown in Figure 4B. Arifovic et al. (2006) indicate that standard learning algorithms have limited success in capturing the alternation between the two pure-strategy Nash equilibria in the Battle of the Sexes game. Yet in the proposed model, automata predominantly converge on alternating behavior between the two actions. Finally, a few pairs converged to one of the two pure-strategy Nash equilibria. Figure 4C provides information on the speed of convergence. The automaton pairs can be classified into two groups: (1) those which converged to alternations, and (2) those which converged to one of the pure-strategy Nash equilibria. The pairs that converged to alternations are denoted by the green dashed line at a payoff of 0 (i.e., players within the pairs earned the same payoff). These pairs converged in less than 28,000 periods. On the other hand, the pairs which converged to one of the two pure-strategy Nash equilibria are denoted by the green dashed line at a payoff of 2. The latter pairs took between 28,000 and 34,000 periods to converge.


Learning with repeated-game strategies.

Ioannou CA, Romero J - Front Neurosci (2014)

Battle of the sexes.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4115627&req=5

Figure 4: Battle of the sexes.
Mentions: The payoff matrix of the Battle of the Sexes game is indicated in Figure 1B. In this game, there are two pure-strategy equilibria: (A, B) and (B, A). Figure 4 shows the results of the simulations. In particular, Figure 4A shows the relative frequency of automaton pairs played over the last 1000 periods. The plot covers a large number of automata although Automaton 12 and Automaton 18 show up most frequently. Automaton 12 switches actions every period unless both players choose B in the previous period. Automaton 18 switches actions every period unless both players choose A in the previous period. Therefore, a pair consisting of Automaton 12 and Automaton 18 would end up alternating between the two pure-strategy Nash equilibria of the stage game. Each automaton would thus earn an average payoff of 3. This is shown in Figure 4B. Arifovic et al. (2006) indicate that standard learning algorithms have limited success in capturing the alternation between the two pure-strategy Nash equilibria in the Battle of the Sexes game. Yet in the proposed model, automata predominantly converge on alternating behavior between the two actions. Finally, a few pairs converged to one of the two pure-strategy Nash equilibria. Figure 4C provides information on the speed of convergence. The automaton pairs can be classified into two groups: (1) those which converged to alternations, and (2) those which converged to one of the pure-strategy Nash equilibria. The pairs that converged to alternations are denoted by the green dashed line at a payoff of 0 (i.e., players within the pairs earned the same payoff). These pairs converged in less than 28,000 periods. On the other hand, the pairs which converged to one of the two pure-strategy Nash equilibria are denoted by the green dashed line at a payoff of 2. The latter pairs took between 28,000 and 34,000 periods to converge.

Bottom Line: In the Prisoner's Dilemma game, we find that the strategy with the most occurrences is the "Grim-Trigger." In the Battle of the Sexes game, a cooperative pair that alternates between the two pure-strategy Nash equilibria emerges as the one with the most occurrences.In the Stag-Hunt and Chicken games, the "Win-Stay, Lose-Shift" and "Grim-Trigger" strategies are the ones with the most occurrences.Overall, the pairs that converged quickly ended up at the cooperative outcomes, whereas the ones that were extremely slow to reach convergence ended up at non-cooperative outcomes.

View Article: PubMed Central - PubMed

Affiliation: Department of Economics, University of Southampton Southampton, UK.

ABSTRACT
We use the self-tuning Experience Weighted Attraction model with repeated-game strategies as a computer testbed to examine the relative frequency, speed of convergence and progression of a set of repeated-game strategies in four symmetric 2 × 2 games: Prisoner's Dilemma, Battle of the Sexes, Stag-Hunt, and Chicken. In the Prisoner's Dilemma game, we find that the strategy with the most occurrences is the "Grim-Trigger." In the Battle of the Sexes game, a cooperative pair that alternates between the two pure-strategy Nash equilibria emerges as the one with the most occurrences. In the Stag-Hunt and Chicken games, the "Win-Stay, Lose-Shift" and "Grim-Trigger" strategies are the ones with the most occurrences. Overall, the pairs that converged quickly ended up at the cooperative outcomes, whereas the ones that were extremely slow to reach convergence ended up at non-cooperative outcomes.

No MeSH data available.


Related in: MedlinePlus