Decision Making In Prisoner’s Dilemma

1.2 Practical part

In sections 8.-12. we will deal with individual hypotheses, as well as with the experimental designs and theoretical considerations that are associated with the particular hypotheses. We will test experimentally the difference between single-move and iterated Prisoner’s Dilemma game in terms of the amount of cooperation – see section 8. We will try to determine whether there is an effect of learning (see section 10.), and of explicit, non-binding communication, or “cheap-talk” (section 11.) on decision making in the Prisoner’s Dilemma. In section 9. we will examine the existence and extent of the so called end-effect in the iterated Prisoner’s Dilemma game. We will also perform some (preliminary) regression studies using data from our experiments and measures of certain characteristics of the players (friendliness, risk avoidance, dominance, and tolerance for ambiguity) obtained by self-rating scales in section 12.

I. Theoretical part

2. Classical utility theory and classical decision making

2.1 Mathematically calculated utility

According to expected utility theory (or classical utility theory), rational decision maker is willing to invest $5, if he has 100% certainty to earn at least $5, and also if he has 50% probability to earn at least $10 (or a 5% probability to earn $100, etc.). It is true for all goods and things of value, such as time, effort, or acts of friendship. This rule represents the most simple form of rational decision making.

Graphic representation of the expected utility value function is a linear function (see Graph 2.1). The more goods you get, the higher the utility (value) you perceive. A rational decision maker chooses the alternative with the highest value perceived, that is with the highest amount of consumption (or yield), all else being equal – this is called utility maximization.
Graph 2.1: Expected utility value function f

2.2 Expected utility with diminishing returns

Economic theory discovered that perceived utility does not in facet rise linearly (and infinitely) with consumption (yield). This finding was formulated as the law of diminishing returns. The law of diminishing returns (also law of diminishing marginal returns or law of increasing relative cost) states that in all productive processes, adding more of one factor of production, while holding all others constant, will at some point yield lower per-unit returns (see for example Samuelson, 1991, pp. 447-448). The law applies to monetary investment, as well as to acts of friendship, or to eating chocolate, it applies to production, as well as consumption.

Graphic representation of the expected utility value function with diminishing returns is the function depicted in Graph 2.2. The interpretation is the same as for Graph 2.1 function, only for higher amounts of consumption (yield) the perceived utility rises less and less steeply.
Graph 2.2: Utility value function f with diminishing returns

Since obtaining a unit of consumption (yield) may require a unit of some investment, and since the function of perceived cost of investment may rise linearly with the amount of consumption, while the function of perceived utility tends to rise less steeply with growing consumption, the decision maker might stop consuming at a certain moment (see Graph 2.3).

Graph 2.3: Investment and consumption/yield functions

Graph 2.3 depicts the function of perceived utility (f_u) of consumption (or yield) and the function of perceived cost of investment (f_i) necessary to acquire that consumption (yield). The net perceived utility equals f_u – f_i. As you can see, when point B is reached, the net perceived utility becomes negative, and the decision maker stops further consumption (and investment).

3. Bounded rationality theory

3.1 Bounded rationality vs. classical utility theory

One of the most prominent and insightful critics of modern mainstream economic theory of rationality is Herbert A. Simon. Economic theory predicts behavior as a function of environment without taking into account empirical findings about actual human actors (Simon, 1979, 1990, 2001). This dominant stream of economic theory leads to Utopian results, not corresponding with empirical data about human behavior and bounded character of human rationality (Simon, 2001). Among other authors pointing out the limited cognitive and reasoning powers of human species with respect to certain problems (sometimes called cognitive closure) were for example Chomsky (1975), Fodor (1983), or McGinn (1991).

Simon reviews examples of mathematically highly sophisticated theoretical work of modern mainstream economic theory: Arrow and Debreu (the impossibility theorem, optimizing equilibrium), von Neumann (game theory, see von Neumann and Morgenstern, 2004), Robert Lucas (rational expectation), Sholes and Merton (rational speculation) (Simon, 2001). He, however, values much higher those “simpler” and “less profound” works that capture more realistically and accurately the actual psychology and behavior of decision makers (and procedural aspects of their decision making), such as empirical research and theory by Kahneman and Tversky (see below), Vernon A. Smith (experimental markets), or Selten (experimental game theory – more on experimental game theory in section 6.
Simon showed (1978a) that mathematically rigorous rendering of economic or decision problems (e. g. auctorial mathematics) can be often transformed into simpler and more palatable functional description (e. g. postulating attitudes, such as risk aversion, that can explain why people buy insurance) without any substantial information or inferential loss. Take for example his early paper (A Formal Theory of the Employment Relation, 1951 – see Simon 1978a, p. 5), where he proved with help of fifteen equations describing maximizing behavior of employer and employee, why people should prefer employment contract to ordinary sales contract, while the functional argument is in fact pretty simple – stable employment contract protects both employer and employee against certain kinds of uncertainty: the employee has secured income, and the employer can postpone his decisions about the employee’s agenda, whenever strategically advantageous (e. g. when decisions’ outcomes are contingent on future uncertain events) (Simon, 1978a, p. 5).