L>Non-Zero-Sum Games
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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 sầu 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 lớn all others, nor isthere a predictable outcome. Non-zero-sum games are alsonon-strictly competitive, as opposed lớn the completely competitivezero-sum games, because such games generally have sầu both competitivevà cooperative elements. Players engaged in a non-zero sum conflicthave some complementary interests & 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 & his wife want to go outfor the evening. They have sầu decided to lớn go either lớn a ballet or to aboxing match. Both prefer to lớn go together rather than going alone.While the man prefers to lớn go to the boxing match, he would prefer togo with his wife khổng lồ the ballet rather than go to the fight alone.Similarly, the wife would prefer to lớn go to the ballet, but she toowould rather go to the fight with her husbvà than go lớn the balletalone. The matrix representing the game is given below:Husband 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 sầu, it can be seen that the situationrepresents a non-zero-sum, non-strictly competitive sầu conflict. Thecomtháng interest between the husbvà và wife is that they would bothprefer khổng lồ be together than lớn go khổng lồ the events separately. However,the opposing interests is that the wife prefers lớn go to the balletwhile her husbvà prefers khổng lồ go to lớn the boxing match. Analyzing a Non-Zero-Sum Game Communication It is conventional belief that the ability to communicate could never work to lớn a player"s disadvantage since a player can always refuse lớn exercise his right lớn communicate.


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However, refusing khổng lồ communicate is different from an inability lớn communicate. The inability khổng lồ communicate may work to lớn a player"s advantage in many cases. An experiment performed by Luce and Raiffa compares what happends when player can communicate & 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 và Bob cannot communicate, then there is no possiblity of threats being made. So, Susan can vị no better than to play strategy A và Bob can vày 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 lớn playing strategy b. If Bob submits, Susan will gain 2 & Bob will thua trận 1 (as opposed to Susan gaining 1 và Bob gaining 2 when communication is not allowed). Restricting Alternatives The Battle of the Sexes example given above sầu seems to lớn be an unsolvable dilemma. However, this problem can be solved it either the husbvà 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 lớn the boxing match, the husbvà would have sầu to go to lớn the ballet along with his wife in order lớn maximize his self-interest. Because the wife bought the two tickets, the husbands optimal payoff, now, would be khổng lồ go along with his wife. If he were lớn 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 lớn 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 và Stag Hunt
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