Cheap Talk Coordination Game

• Content map: SMU H3 Game Theory Map

Setup

Definition:

Cheap Talk Coordination Game

• Players: Two players, Player 1 and Player 2.
• Strategies: Player 1 sends a costless message: Starbucks or Local Latte, then chooses an action; Player 2 chooses an action after observing the message.

Rules

• Start with a costless message before an assurance game; Players send or observe the message and then choose Starbucks or Local Latte.
• Players make a non-binding cheap-talk announcement before choosing actions.
• The message has no direct payoff effect.
• After communication, the players play the underlying assurance game.

Payoff Matrix

Derivation (Best Response Analysis)

• In the underlying assurance game:
  • if the other player goes to Starbucks, the best response is Starbucks,
  • if the other player goes to Local Latte, the best response is Local Latte.
• If Player 1 says “Local Latte” and both players intend to follow that message, then:
  • Player 2 best responds by choosing Local Latte because $2>0$,
  • Player 1 best responds by also choosing Local Latte because deviating to Starbucks gives $0<2$.
• Cheap talk can therefore coordinate play on the efficient equilibrium.
• However, messages can also be ignored:
  • If both players always choose Starbucks regardless of the message, neither wants to deviate after communication stage.
  • Starbucks is still a Nash equilibrium of the base game.

Derivation (Nash Equilibrium)

• A communication-following equilibrium exists in which:
  • Player 1 says “Local Latte”,
  • Player 1 then chooses Local Latte,
  • Player 2 chooses whatever location Player 1 announced.
• Bubbling equilibria also exist in which messages are sent but ignored in play.

Nash Equilibrium

Result:

The cheap-talk extension has multiple subgame perfect equilibria:

• An informative equilibrium that coordinates on (Local Latte, Local Latte),
• Bubbling equilibria in which messages are ignored and play settles on an equilibrium of the underlying game such as (Starbucks, Starbucks).

Social Optimum

• (Local Latte, Local Latte) yields total payoff $4$.
• (Starbucks, Starbucks) yields total payoff $2$.
• Therefore the socially optimal coordination point is Local Latte.

Insights

Insight:

• Cheap talk works when players want to coordinate on the same action.
• Communication does not eliminate multiplicity because non-informative equilibria remain feasible.