L>Non-Zero-Sum Games
The theory of zero-sum games is vastly different from that ofnon-zero-sum games because an optimal solution can always be found. However, this hardly represents the conflicts faced in the everydayworld. Problems in the real world do not usually havestraightforward results. The branch of Game Theory that betterrepresents the dynamitienkiem.com.vn of the world we live in is called the theoryof non-zero-sum games. Non-zero-sum games differ from zero-sum gamesin that there is no universally accepted solution. That is, there isno single optimal strategy that is preferable to all others, nor isthere a predictable outcome. Non-zero-sum games are alsonon-strictly competitive, as opposed to the completely competitivezero-sum games, because such games generally have both competitiveand cooperative elements. Players engaged in a non-zero sum conflicthave some complementary interests and some interests that arecompletely opposed.A Typical ExampleThe Battle of the Sexes is a simple example of a typicalnon-zero-sum game. In this example a man and his wife want to go outfor the evening. They have decided to go either to a ballet or to aboxing match. Both prefer to go together rather than going alone.While the man prefers to go to the boxing match, he would prefer togo with his wife to the ballet rather than go to the fight alone.Similarly, the wife would prefer to go to the ballet, but she toowould rather go to the fight with her husband than go to the balletalone. The matrix representing the game is given below:
Boxing Match   Ballet   Wife   Boxing Match   2, 3 1, 1 Ballet 1, 1 3, 2 The wife”s payoff matrix is represented by the first element of theordered pair while the husband”s payoff matrix is represented by thesecond of the ordered pair.From the matrix above, it can be seen that the situationrepresents a non-zero-sum, non-strictly competitive conflict. Thecommon interest between the husband and wife is that they would bothprefer to be together than to go to the events separately. However,the opposing interests is that the wife prefers to go to the balletwhile her husband prefers to go to the boxing match. Analyzing a Non-Zero-Sum Game Communication It is conventional belief that the ability to communicate could never work to a player”s disadvantage since a player can always refuse to exercise his right to communicate.
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However, refusing to communicate is different from an inability to communicate. The inability to communicate may work to a player”s advantage in many cases. An experiment performed by Luce and Raiffa compares what happends when player can communicate and when players cannot communicate. Luce and Raiffa devised the following game: a b A   1, 2 3, 1 B 0, -200 2, -300 If Susan and Bob cannot communicate, then there is no possiblity of threats being made. So, Susan can do no better than to play strategy A and Bob can do no better than to play strategy a. Susan, therefore gains 1 and Bob gains 2. However, when communication is allowed, the situation is complicated. Susan can threaten Bob by saying that she will play strategy B unless Bob commits himself to playing strategy b. If Bob submits, Susan will gain 2 and Bob will lose 1 (as opposed to Susan gaining 1 and Bob gaining 2 when communication is not allowed). Restricting Alternatives The Battle of the Sexes example given above seems to be an unsolvable dilemma. However, this problem can be solved it either the husband or the wife resticts the others” alternatives. For example, if the wife buys two tickets for the ballet, indicating that she is definitely not going to the boxing match, the husband would have to go to the ballet along with his wife in order to maximize his self-interest. Because the wife bought the two tickets, the husbands optimal payoff, now, would be to go along with his wife. If he were to go to the boxing match alone, he would not be maximizing his self-interest. The Number of Times the Game is “Played” If the game is played only once, players do not have to fear retaliation from their opponents, so they may play differently than they would in a game played repeatedly. Examples of Typical Non-Zero-Sum Games: Prisoner”s Dilemma Chicken and Volunteer”s Dilemma Deadlock and Stag Hunt
