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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

Stag-hunt.
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Figure 5: Stag-hunt.

Mentions: The payoff matrix of the Stag-Hunt game is indicated in Figure 1C. In this game, there are two pure-strategy Nash equilibria: (A, A) and (B, B). However, outcome (A, A) is the Pareto dominant equilibrium. Figure 5 shows the results of the simulations. The relative frequency of automaton pairs in Figure 5A suggests that a relatively small set of automata was chosen. Automaton 5, which implements the “Win-Stay, Lose-Shift” strategy, and Automaton 6, which implements the “Grim-Trigger” strategy were the ones with the most occurrences. Other automata that were chosen frequently included: Automaton 1, Automaton 3, Automaton 4, and Automaton 26. It is important to note that with the exception of Automaton 26, any pair combination from this small set of automata yields a payoff of 3 as both players choose (A, A) repeatedly. Automaton 26 paired with Automaton 26 corresponds to alternating between the two pure-strategy Nash equilibria, which yields an average payoff of 2. Figure 5B confirms that the most likely outcome is for both players to choose A repeatedly. Note that there is also a small number of pairs that converged to (2, 2). Figure 5C shows that convergence in the Stag-Hunt game was quite fast. More specifically, 90% of the pairs converged within only 6000 periods. The blue solid line oscillates mostly between an average payoff of 3 and an average payoff of 2, while the green dashed line indicates that, in either case, the average payoff difference of the automaton pairs was 0.


Learning with repeated-game strategies.

Ioannou CA, Romero J - Front Neurosci (2014)

Stag-hunt.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 5: Stag-hunt.
Mentions: The payoff matrix of the Stag-Hunt game is indicated in Figure 1C. In this game, there are two pure-strategy Nash equilibria: (A, A) and (B, B). However, outcome (A, A) is the Pareto dominant equilibrium. Figure 5 shows the results of the simulations. The relative frequency of automaton pairs in Figure 5A suggests that a relatively small set of automata was chosen. Automaton 5, which implements the “Win-Stay, Lose-Shift” strategy, and Automaton 6, which implements the “Grim-Trigger” strategy were the ones with the most occurrences. Other automata that were chosen frequently included: Automaton 1, Automaton 3, Automaton 4, and Automaton 26. It is important to note that with the exception of Automaton 26, any pair combination from this small set of automata yields a payoff of 3 as both players choose (A, A) repeatedly. Automaton 26 paired with Automaton 26 corresponds to alternating between the two pure-strategy Nash equilibria, which yields an average payoff of 2. Figure 5B confirms that the most likely outcome is for both players to choose A repeatedly. Note that there is also a small number of pairs that converged to (2, 2). Figure 5C shows that convergence in the Stag-Hunt game was quite fast. More specifically, 90% of the pairs converged within only 6000 periods. The blue solid line oscillates mostly between an average payoff of 3 and an average payoff of 2, while the green dashed line indicates that, in either case, the average payoff difference of the automaton pairs was 0.

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