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Understanding Coordination Games: Experimental Insights on Equilibrium Selection Dynamics

This document explores key in-class experiments on coordination games, focusing on equilibrium selection through studies by Van Huyck, Battalio, Beil, and others. It highlights the tests of equilibrium selection, unique vs. multiple equilibria, and discusses empirical findings from various treatment designs, emphasizing strategic uncertainty's role in coordination failures. The results reveal that while players tend to converge on secure yet inefficient outcomes over repeated plays, achieving the first-best payoff-dominance remains unlikely. Insights are drawn from different game configurations, shedding light on players' decision-making processes.

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Understanding Coordination Games: Experimental Insights on Equilibrium Selection Dynamics

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  1. Outline • In-Class Experiment on a Coordination Game • Test of Equilibrium Selection I :Van Huyck, Battalio, and Beil (1990) • Test of Equilibrium Selection II :Van Huyck, Battalio, and Beil (1991) • Test of Equilibrium Selection III : Copper, DeJong, Forsythe, and Ross (1990)

  2. From Unique Equilibrium  Multiple Equilibria • pBC, Centipede Game  Unique Nash equilibrium • People do not play the unique Nash equilibrium • Every strategy is a Nash equilibrium (i.e., Nash does not produce a sharp prediction)

  3. The Weakest-Link Game • n players • Strategy space =

  4. Game A: a =$0.2, b=0.1, c=$0.6

  5. Hypotheses: Deductive vs. Inductive Principles • Payoff Dominance • Security (Maximin} • History dependent • For t > 1, minimum (t) = minimum (1) =

  6. Game B: a=$0.2, b=$0.0, c=$0.6

  7. Experimental Design * Only minimum was announced after every round

  8. Hypotheses • Payoff Dominance: {7, …, 7} in A and B • Security (Maximin}: {1,…, 1} in A but not in B • For t > 1, minimum (t) =

  9. Results of Treatment A

  10. Results of Treatment A

  11. Results of Treatment B and A’

  12. Results of Treatment C: Fixed Pairings

  13. Results of Treatment C: Fixed Pairing

  14. Experimental Design * Only minimum was announced after every round

  15. Results of Treatment C: Random Pairings

  16. Full Distribution of Choices

  17. Summary • The presence of strategic uncertainty (2 possible equilibrium selection principle) results in coordination failure and inefficient outcome • The first-best outcome of payoff-dominance is unlikely, both initially and with repeated plays • With repeated plays, subjects converge on secure but the most inefficient equilibrium

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