which case its payoff will be 0. On the other hand, if B selects B3, the maximum payoff for it will be $18 million, provided that A selects A2 and there is no possibility of a $0 payoff. Therefore, B will select B3. What will A select? A will no doubt select A3 because it will produce a payoff of $5 million for B, the smaller of the two payoffs. The final solution of the game will be B3 for B and A2 for A. Unfortunately, B comes out much worse off in this case even though it had the first option to move.
Interestingly, however, if we keep the objectives of the two communities the same as before, where A will try to maximize its gains and B minimize its losses from the set of choices they will make, the final solution, with B making the first move, will be B2 for B and A2 for A. The equilibrium values corresponding to this will be $15 million for A and $10 for B. In other words, the outcome of the game will be the same as the one under dominant strategies, given the nature of the payoff matrix we have in this example.
In government, as in the private sector, decisions are often made with limited knowledge or information. When information is not available fully and completely, the decision one would have to make with insuffient information will invariably affect the results it would produce. In most instances, the results will be probabilistic rather than deterministic. In other words, there will be uncertainty in the results, although the degree of uncertainty will vary from situation to situation. This chapter has presented a brief discussion of several commonly used methods for dealing with the problems of uncertainty. Three types of uncertainty were presented here: partial uncertainty, complete uncertainty, and conflict. For each type, several different methods were discussed, ranging from expected value to Bayesian statistics to game theory.
Of these, game theory deserves special attention because of its widespread application. As a theory, it is both challenging and dynamic. For instance, it can deal with games that are zero-sum as well as those that are non-zero-sum, although much of our discussion here focused on zero-sum games. It can also deal with games that involve only two players as well as games that involve n number of players, although n-person games are much more difficult to operationalize. Finally, it can deal with games where the players have both partial as well as full information on all their strategies, including those of their opponents. As we have seen, games with partial information are far more complex than games with complete information.