Sequential games and strategic moves

Abstract

Life can only be understood backwards, but it must be lived forwards. Soren Kierkegaard, 1843 IN MANY interactive situations, the main concern is for each player to figure out how others will respond to one's own moves and anticipate where their decisions will eventually lead. The games introduced so far have not been adequate at elucidating how a series of moves by each player produces an outcome, as players move at the same time. In a game where players make their decisions simultaneously without knowing the other player's decision, it is interactive only with their current thinking about the other's present move and vice versa. If actions are arranged in a determined temporal order, the sequence of play can be represented in an extensive form displaying a choice at every decision point. It is an important departure from simultaneous games represented in the form of a payoff matrix. In general, a strategy in an extensive form game is constituted by a sequence of actions referred to as moves. In this chapter our main focus is on sequential games that allow the players to move one after another. In tacit bargaining, nonverbal cooperation on a particular solution can arise from a process based on a move and a countermove. The choices of later players are contingent upon the moves made earlier by the other player. This time difference in actions has a strategic effect, as illustrated in the extensive form of a game of Chicken and Battle of the Sexes. At the same time, a player may devise a move outside the defined actions of a given game to gain a strategic advantage. As revealed in the chapter's last section, a chance element needs to be incorporated in the event that players are not able to see all the prior moves made by other players. Sequential games In a sequential-move game, each player sees what their opponent has done before choosing their next action. Having the knowledge of the other players' previous move makes all the difference in a strategic interaction. The order of moves is encapsulated in a decision tree which represents how a game is to be played out over the course of a particular event (O'Neill 1999). A game tree reveals who moves when, and which sequences of actions result in what kind of outcomes.