Game Theory: Coordination, Dilemmas, and Nash Equilibria

Posted on Mar 17, 2026 in International Business Economics

1. Pure Coordination Game

In a pure coordination game, players have identical interests and must “sync up” on the same strategy to achieve the best outcome.

  • Characteristics: Multiple Nash equilibria exist where players choose the same action.
  • Payoffs: (1,1) if both choose A or both choose B; (0,0) if they mismatch.

2. Assurance Game (Stag Hunt)

This is a coordination game with a risk element where the highest joint payoff requires trust.

  • Characteristics: Two pure Nash equilibria. One is Pareto dominant (highest total payoff), while the other is risk-dominant (safer if you lack trust).
  • Payoffs: (5,5) if both hunt Stag; (3,3) if both hunt Hare. If one hunts Stag while the other hunts Hare, the Stag hunter gets 0.
  • Difference: Unlike pure coordination, one equilibrium is clearly better, but it requires assurance that the other will cooperate.

3. Battle of the Sexes

This represents coordination with a conflict of interest.

  • Characteristics: Two pure Nash equilibria. Players want to coordinate, but they disagree on where.
  • Payoffs: Player 1 prefers (2,1), while Player 2 prefers (1,2). If they go to different places, they get (0,0).
  • Difference: It is harder than pure coordination because players must negotiate who gets their preferred outcome.

4. Prisoner’s Dilemma

In this scenario, there is a dominant strategy to defect or cheat.

  • Payoffs: The only Nash equilibrium is (Defect, Defect), even though (Cooperate, Cooperate) would yield a higher payoff for both.
  • Difference: The Nash equilibrium is not Pareto efficient. It is the only game here where the rational “best response” leads to a strictly worse outcome for the group.

5. Chicken Game

These are anti-coordination games where it is mutually beneficial for players to play different strategies. There are three Nash equilibria.

6. Centipede Game

Although the total pot grows, the player whose turn it is can always get a slightly higher payoff by stopping now than they would if they continued and the other player stopped in the very next turn.

Best Response and Dominance

  • Strictly Dominated: Never a best response. If a strategy is strictly dominated, it can never be a best response to any opponent’s move.
  • Nash Equilibrium (NE): Must be a best response. If a strategy is part of a Nash equilibrium, it must be a best response to what the other players are specifically doing.
  • The “Trap”: A strategy can be a “Best Response” to one specific move, even if it is not played in any Nash equilibrium.
  • Weakly Dominated: Another strategy is better or equal. Do not eliminate these; they can be part of an NE.

Average Plus One and 2/3 Average Games

When comparing the target outcome, if the target is lower than the average, it goes to zero; if higher, it goes to the maximum. There will be one strictly dominated strategy.

Strategic Tips

  1. Strategies vs. Outcomes: A strategy is a complete contingency of what each player should do in every situation, while an outcome is what actually plays out.
  2. Defining Outcomes: An outcome is the vector of actions taken by each player. When asked for an outcome, provide the actions; numerical payoffs are secondary.
  3. General Solutions: Get comfortable providing general solutions for proofs. If an outcome is not a Nash equilibrium, providing a specific counter-example can save time and cognitive effort.