# Games — all about Utilities

December 26, 2011 Leave a Comment

it has been a while…

A game’s outcome is measured in its utility; i.e. user 1 utility vs. user 2 utility. Utility is the classification of decision making when it comes to games. This goes back to the early days of Game theory and it was put forth (coined really) by von Neumann and Morgenstern. “Utility” is a very overused term, but it has specific meaning in this context. Others have also contributed to this concept, and one can refer to Savage (1954) for a great history of this term.

As with anything else – one must consider the risk vs. reward for a given action. For a game, this notion is taken one step further as a given strategy or action may have one of the following clasifications:

– Certainty – or – Certain outcome: each action is known to invariably lead to a specific and set outcome. “you know exactly what you will receive if you employ Strategy S1”. This class of decision making is very popular – it turns out. much of formal theory in economics, psychology and management can be classified here.

– Uncertainty – or – Uncertain outcome: either player’s strategy is could lead to one of many outcomes, but the distribution of these outcomes is not known prior. “Strategy s2 could lead to outcome x, y, and z – but not sure if the % for each is the same”

– Risk: each action leads to one of many outcomes, *and* the probability of occurrence of each outcome is known. A coin toss could lead to a reward of $10 if it comes up heads, and $5 if it comes up tails.

Utility relates to classes of games that fall under uncertainty and risk. von Neumann and Morgenstern claimed that a person’s affinity towards risk and its behavior or actions to a given game relates to the utility of the expected value. More specifically speaking, if one is able to have (and continue to have) a preference between two outcomes, then one is guided entirely by the utility of the expected outcome. In other words, utility can be measured when one is “acting in accord with his true taste”.

If the payout for a game is $5 and $10 – according to the level of risk of each action, one person might be risk averse, and continue to “bet” on $5, whereas the other person might be willing to risk for a $10 outcome. Person 1’s action leads up to believe that his utility for $5 is higher than the second person’s utility for $10. In other words, person 1 might not be financially capable of risking $5, where as the second person is more willing to give up $5 to have the chance of winning $10.

We will come back to this term over and over again thruout.

Art Sedighi