2x2 Games - LLM Arena

2x2 GAMES

VS

Offline

Round History

Launch a game to see round history

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ROUND / 10

PLAYER 1

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0

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VS

PLAYER 2

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Payoff Matrix (P1, P2) - Battle of the Sexes

A

B

A

(A, A)

(A, B)

B

(B, A)

(B, B)

Outcome Frequencies

(A,A)

0

0%

(A,B)

0

0%

(B,A)

0

0%

(B,B)

0

0%

Avg P1: 0.00

Avg P2: 0.00

LLM Reasoning

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Player 1

Player 2

Select a round to view LLM reasoning

How It Works

Two players simultaneously choose action A or B. The payoff each player receives depends on both players' choices, as shown in the payoff matrix.

Each cell shows (P1 payoff, P2 payoff). The highlighted cell shows the outcome of the current round.

Game Types

Game	Description
Battle of the Sexes	Coordination game - both prefer to match, but disagree on which outcome is best
Prisoner's Dilemma	Classic dilemma - mutual cooperation (A,A) is better than mutual defection (B,B), but defecting is individually rational
Second Best	Players' first choices differ, creating tension between individual and collective optimality
Unfair / Biased	Asymmetric games where one player has an inherent advantage
Matching Pennies	Zero-sum game with no pure Nash equilibrium - P1 wins if actions match, P2 wins if they differ
Win-Win	Coordination game where players can achieve mutual benefit
Custom	Edit payoff values directly to create any 2x2 game

Nash Equilibrium

A Nash equilibrium is an outcome where neither player can improve by unilaterally changing their choice. Some games have one equilibrium, some have multiple, and some have none in pure strategies.

Tips

Watch how LLMs reason about strategic situations in the right panel. Do they find the Nash equilibrium? Do they attempt cooperation? How do they adapt over multiple rounds?