Game Theory: A Critical Introduction

So far in this book we have been subjecting almost every theoretical proposition of game theory to scrutiny. The result has been a sequence of challenges and defences of the theory’s predictions about how rational people would play the games under study. What would be more natural then than to ask real people to play these games under controlled (laboratory) conditions so that we can observe their actual behaviour? Would this not cut through the maze of arguments surrounding the appropriateness of the various assumptions, such as CKR (Common Knowledge of instrumental Rationality), CAB (Common Alignment of Beliefs) and the resultant Nash equilibrium, the marriage of backward induction and CKR, as well as the initial assumption that players are exclusively instrumentally rational? Indeed our reflections on the assumptions of game theory are based on mental experiments of the sort: ‘How would I behave in this situation? What would I expect my opponent to do?’ Such introspection is a type of proto-experiment. Well-organised experiments involving many people is the next step.

In fact several central propositions in game theory have been systematically tested through laboratory experiments. In this chapter we report on some of the results. Most experiments are typically organised around one particular type of game and then the observed behaviour of individuals and groups is used to test a number of hypotheses. Faithful to this format, we begin the discussion in section 8.2 with evidence on backward induction (see Chapter 3). Does the marriage of CAB (the assumption that beliefs will always remain consistently aligned) with backward induction (see sections 3.2 and 3.3) predict how well people play these games? Or will they deviate from the theory’s predictions, as we described in section 3.4? In section 8.3 we turn to the prisoners’ dilemma (see Chapters 5 and 6), in particular the finitely repeated version. How relevant are the stories about the possibility

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