7 Some Classic Games of Iterated Dominance
Before diving into the deep pool of behavioral game theory, we need some specific nomenclature about what constitutes a game and its solution, or what we have been calling its equilibrium. If you’ve ever played a board or card game with your friends or family, then none of this terminology should surprise you.
A game consists of a set of “players,” each with their own set of “strategies.” Precise “rules” govern the “order” in which players make their “moves,” the “information” they have available, and, ultimately, their “payoffs.” I don’t know about you, but the card game poker comes immediately to mind. The keywords are players, strategies, rules, order, moves, information, and payoffs.
We expect that Homo economicus will attain what’s known as a Nash equilibrium, or perhaps a refinement of Nash equilibrium, depending upon the game being played.[1] Simply put, a Nash equilibrium prevails when each player can no longer adjust his or her strategy to obtain added payoff. Thus, in a Nash equilibrium, all players have chosen respective strategies that are the best responses to each of the other players’ strategies. The Nash equilibrium is derived analytically and, thus, is highly predictable. We will see just how predictable the equilibrium is in a wide variety of games. Since this is the equilibrium obtained by Homo economicus, we henceforth use the terminology Homo economicus and “analytical equilibrium” inter-changeably.
As we will learn, the equilibria typically obtained in games played by Homo sapiens expand upon the Nash equilibrium concept by adding in such aspects of the human experience as emotion, miscalculation, limited foresight, doubt about how informed the other players are, and learning-by-doing—many of the same human quirks and idiosyncrasies we encountered in Section 1. The equilibria obtained in games played by Homo sapiens are typically derived more intuitively than analytically. Thus, the equilibria are generally unpredictable.
Let’s start with one of the most famous and basic of games—ultimatum bargaining.
Ultimatum Bargaining
Consider the following game presented in Camerer (2003):[2]
The analytical equilibrium for this game evolves according to the following logic:
By going first, the Proposer possesses all of the bargaining power. The Proposer, therefore, exploits the fact that the self-interested Responder will take whatever is offered. The amount offered by the Proposer is thus very close to zero. Surmising that this is indeed the Proposer’s best strategy, and also recognizing that he gets nothing if he rejects the Proposer’s offer, the Responder has no better strategy than to accept whatever the Responder offers, as meager as the offer is. The Proposer knows that this is the logic the Responder will use, and the Proposer knows that the Responder knows this, and so on. Hence, the analytical equilibrium is that the Proposer makes the meager offer (in the limit, $0.01) and the Respond