Module 5 Introducing Uncertainty into games of strategy
5.2 Risk attitudes, beliefs, and payoffs
This clip explains how a player’s attitude towards risk can be incorporated into the “payoffs” for players in strategic games.
The key idea here is using the graphical “connect the dots” approach to thinking about players’ preferences under uncertainty. A player faces a risk, described by a personal belief about the chances of an event (eg clubs or spades, stock market up or stock market down) or some behaviour (in the Princess Bride, will Wesley put the poison in the cup in front of him or the cup in front of me? Has Wesley developed an immunity to the iocane poison?) and some relevant consequences (eg monetary losses or gains, or, as in the Princess Bride….life or death). How can we come up with a payoff number that represents the “value” of that risk (for good or for ill) for a player ?
We develop a certainty equivalent approach to valuation (most game theory texts don’t take this approach, they use expected utility theory – but at our introductory and interdisciplinary level, EU theory and its’ alternatives, Prospect Theory, are too much of a deviation for us to take) . Straight lines between “dots” represent risk neutral attitudes; two types of curved lines between dots represent risk averse or risk seeking attitudes.