Game Theory II: Axelrod's Tournaments - Gateway, Lecture 4

Vocabulary flashcards covering key terms, strategies, tournaments, and concepts from the Axelrod lecture notes.

ALL D

Defects every round, regardless of the opponent.

ALL C

Cooperates every round, regardless of the opponent.

RANDOM

A strategy that defects or cooperates with equal probability (50% each) each round.

Best response to ALL C

ALL D.

Best response to ALL D

ALL D again.

Best response to RANDOM

ALL D.

Robust strategy

A strategy that performs well across a range of opponents and conditions, not tied to a single scenario.

Axelrod's Tournament

A competition to find robust strategies in a 200-round Prisoner’s Dilemma by pitting submitted strategies against themselves, RANDOM, and all others.

Tournament format (1st tournament)

Experts submit strategies; each faces itself, RANDOM, and all others in a 200-round PD; highest final score wins.

1st Tournament Goal

Find a strategy that’s robustly successful.

DOWNING

Defects on unresponsive players; starts with a double defection.

FRIEDMAN

Starts by cooperating; if ever defected on, defects back forever.

TIT FOR TAT (TFT)

Cooperates initially and then copies the opponent’s last move; known for being nice and retaliatory.

JOSS

Like TFT, but with a 10% chance of defecting on a cooperator; performed worse than TFT.

TIT FOR TWO TATS

Defects back only after two defections by the opponent.

LOOK AHEAD

Strategy inspired by chess AIs; won the preliminary tournament described in advertisements.

REVISED DOWNING

Like DOWNING, but with added niceness (more forgiving).

ECOLOGY

Process where after every round, lowest scorers are replaced by copies of the highest scorers; iterated until stable.

The Rachet

It’s easier to increase cooperation than to decrease it.

w (continuation probability)

Probability of the game continuing to the next round; higher w emphasizes the future and the shadow of future payoffs.

Stability (solo)

ALL D is collectively stable; no single other strategy can invade; TFT cannot outperform ALL D in isolation.

Stability (clusters)

A cluster of TIT FOR TATs can take over because mutual cooperation within the cluster outweighs losses to natives (threshold around 5%).

The great asymmetry

Stability varies by population structure: ALL D can be stable against individuals but not against clusters; TFT is stable against clusters.

ALL D collectively stable?

Yes.

ALL D against clusters?

No.

TIT FOR TAT collectively stable?

Yes.

TIT FOR TAT against clusters?

Yes.

The PD (Prisoner’s Dilemma)

A two-player game where defection dominates, but cooperation can yield better joint outcomes; used extensively in Axelrod’s studies.

Equilibria

Strategic outcomes where no player benefits from unilaterally deviating; in PD, mutual defection is a classic equilibrium; repeated PD can yield other equilibria.

Pareto efficiency

An outcome where no one can be made better off without making someone else worse off.

State of nature (Hobbes)

A hypothetical pre-social condition described by Hobbes; life without government is often characterized as harsh; exit from it via covenants and civil society.