PRINCIPLES OF CHOICE IN GAMES AGAINST NATURE

(First Three Principles Apply Directly to Games of Strategy As Well)

Maximax Principle: choose the strategy that is required to get your best possible outcome [depends on ordinal payoffs only]

Maximin Principle: for each possible strategy, determine the worst outcome or minimum payoff you might possibly get (determine your security level for each strategy) and then choose the strategy that gives you the highest security level (i.e., “the maximum of the minimums”) [depends on ordinal payoffs only]

Dominance Principle: if one strategy gives you at least as good an outcome in every contingency as some other strategy and a better outcome in at least one contingency, then don’t choose that other strategy (as it is dominated by the first strategy) — choose an undominated strategy instead. If one strategy dominates every other available strategy, it is dominant and you should choose it. [depends on ordinal payoffs only]

Principle of Insufficient Reason (Maximizing Average Payoff): choose the strategy the gives you the highest average payoff (averaged across contingencies). (This assumes payoffs are cardinally [or intervally] measured, and in effect presumes that all contingencies are equally likely.)

Principle of Expected Utility: chose the strategy that gives you the highest expected utility, weighing each contingency by its objective (decision making under risk) or subjective (decision making under uncertainty) probability. (This assumes that utility is linear to payoffs and is cardinally measured, and that the decision maker has at least subjective probability information.)