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Risk Management and Decision Processes Center

Stochastic and Deterministic Prisoner Dilemma (PD) Experiments

PI/Project Contact: Howard Kunreuther

Project description:

Recent controlled laboratory experiments have compared behavior by pairs of individuals in a prisoners dilemma (PD) game where the outcomes are deterministic and in an IDS game where the only Nash equilibrium is for both individuals to defect if they are maximizing expected value, even though they would both be better off by cooperating. In this sense the IDS game is equivalent to a PD game with stochastic outcomes.

We have run a set of experiments where subjects play a set of games, each consisting of ten rounds. At the end of each game the person is paired with a new anonymous person determined by a random process. Each person makes a decision in each round whether to invest in protection (I) and not invest (NI) (which translates to cooperate or defect respectively in the PD problem). We are interested in comparing behavior of individuals when outcomes are deterministic and when they are stochastic

In the deterministic games the payoffs are determined by the actions of both players and each individual knows what action his/her counterpart has chosen. In the stochastic experiments the outcomes are based on a known probability distribution and are identical in expected value to those in the deterministic game. Payoffs at the end of each round are only determined after both parties make their decisions on whether or not to invest in protection. There are thus two types of risks:

•  the uncertainty as to what the other person will do (I or NI)
•  the uncertainty of the payoffs based on the probability distribution of outcomes

The stochastic games were played in two formats:

Full Feedback: At the end of each round, each person learned what his/her counterpart did
Partial Feedback: No feedback except by looking at the outcome. In some cases it is possible to determine what the other person did.

A comparison of preliminary results of one of the games is shown in Figure 1. A much larger percentage of individuals invested in the deterministic PD game than in the stochastic game. Investment was higher in the partial feedback game than in the full feedback game when outcomes are stochastic. A detailed analyses of the results of this and other games will be undertaken this summer.

Figure 1

Future Research

The interdependent security models to date all assume that individuals make their decisions by comparing their expected benefits (with and without protection) to the costs of investing in security. We are investigating how risk-averse each individual is to determine what impact this has on decisions based on an expected utility model. A growing literature in behavioral economics suggests, however, that individuals make choices in ways that differ from this normative model of choice. Context effects (e.g. investing in protection when the event is a financial loss or when it is a loss from fire) may impact on decisions as to whether or not to cooperate. Decisions made by two persons as a team may be different from a single individual's decision. With respect to protective measures, evidence from controlled field studies and laboratory experiments suggest that many individuals invest in security to gain peace of mind and to relieve anxiety about their perceptions of what might happen to themselves or to others in the event of a security-related incident

The interdependent security model implicitly assumes that the risks faced by the firms in the supply chain are independent of their own behavior rather than being endogenous. In reality, if some firms are known to be more security-conscious than others, they are presumably less likely to be terrorist targets. In this sense, investing in security has similarities to the problem of theft protection: if a house announces that it has installed an alarm, then burglars are likely to turn to other houses as targets instead. Similarly, in the case of a chemical supply chain, terrorists are more likely to focus on targets that are less well protected. Future research should examine how changes in endogenous probabilities affect interdependent security solutions, and the appropriate strategies for improving the performance of individual firms as well as the security of multiple companies whose security is interdependent with others.