The Mixed-Equilibrium Strategies for Zero-Sum Games - Assignment Example

The Mixed-Equilibrium Strategies for Zero Sum Games a) How One Would Expect Optimal Play to Change The mixed-equilibrium is a strategic decision making process, which involves conflict and cooperation in the cause of rational decision making. In this case, the optimal player seeks to gain net losses of the participant. In the case of a partial play, a move is said to be an optimal one if it helps in preserving the optimal outcome of the game. This means that a move is optimal if it leads to the outcome of the game being achieved. This is more so where the player optimally manages to have an optimal outcome of a game (Beckert 673). b) Why Paper is Played One-Half of The Time, and Scissors Both Drop to One-Fourth The reason why paper is played more as compared to scissors is because of the strategy it takes. The game is represented in a matrix of players, strategies and pay-offs. These are clearly represented by the functions that are associated with the payoffs of the players, associated with the combination of their actions. In the case of paper, each player has strategies which are specific as opposed to scissors. This is said to give a direct account of simultaneous accounts of the players without any knowledge of those of the other players. In scissors, the three markers, makes the game more predictable to a player and thus most plays are not keen to proceed with the game once they foresee lose because they can possibly know which player will win and more so, once they manage to establish how many changes have been made (Beckert 570). c) The Payoff Matrix and its Use in Verifying the Strategies Specified in a Mixed-Strategy Equilibrium for the Modified Rock-Scissors-Paper Game The utility theory indicates that there is a reasonable assumption and certain players have certain preferences among the outcomes which are consistent with existence of the utility function. The player judges the outcome based on an average utility of the outcome. This thus helps in creating a justification for such cases. However, a two player can be a difficult one. This may mean that the game is no longer a zero-sum game. This shifts to the utility functions of the two players upon their change of locations (Beech 319). The mixed strategy may aid in the implementation of the random mechanism that is involved, and this is by way of trying to draw a line of distinction by tossing a coin among others. d) Explanation as to Why Rock is Played Less Using Game Theory Concepts Rock is an evolution game theory based application. It seeks to give a definition to the framework of the contests, analysis and strategies. The dynamics of the strategies that are applied in rock are influenced mainly by the quality of competing strategies that are applied. Because of the effect of frequency within which the competing strategies are based, less people play it (Beech 261). It does not explain the complexity of the challenge. This is helpful in understanding the behavior of human in a conflict situation. 2. The Game of Two People Approaching one Another on a Sidewalk a) The Three Nash Equilibrium of the Game As the game theory attempts to respond to behavioral concerns, the Nash equilibrium as a concept, attempts to respond in a situation of a game involving two or more players. It is the case that every player assumes to know equilibrium strategies of other players. It is clear that none of the players has anything to achieve by changing their plan unilaterally (Beckert 592). This is attributed to the fact that each play chooses a strategy which they cannot benefit by changing it. This is what constitutes to the Nash equilibrium. The Nash equilibrium is important for the purpose of analyzing the strategies applied in the cause of the interaction of the decision makers. This is instrumental in forecasting the outcome of decision makers. b) Show that the Payoff From the Mixed Equilibrium is Only Half as Good for Either Player as Either of The Two Pure Equilibria. The game presents a form of cooperation between the players, through the bidding commitment. The chances of winning in a mixed equilibrium are low compared to those of winning in a two pure equilibria. This is attributed to the fact that every play applies its own strategy and tactic which is unique. This makes it more complicated as compared to a two player case (Beech 278). 3. Ultimatum Game a) Whether it Makes a Difference For Player 1 To Divide $ 12, $20 Or $ 100 and The Reason The game is an asymmetrical presentation and how the player divides his money affects the nature of the playoff. The art of dividing is a strategy which a player may employ to influence the other players to change their strategies. The game can either be a zero-sum game where the player fails to increase the available money. There is no change in the amount that he wins or loses. However, in an otherwise case, one may win or lose a hefty amount and this is what is regarded as a constant sum game (Beckert 712). b) Whether it Makes a Difference for One if Player 1 is Offering his own Money, Dividing Money That he Won in a Previous Game or Dividing Money Given to Him for Division and the Reason There are simultaneous games where the player moves at simultaneous pace. In this case, the players are not aware of the players’ actions and they may not influence the strategy. However, where the other players are aware of the actions of the strategies of a player, it changes to a sequential game. c) Whether There is a Difference if Player 1 is an Individual, an Organization or a Computer and the Reason There is a great difference if player one is an individual, an organization or a computer. If the player is an individual, the gene applied in the playing may not compare as to where an organization is playing. Most organizations will apply a combination and on the other hand if it is a computer, it is certain that the program is perfect and this may call for perfect strategies (Beech 315). 4. Discussion of the ‘Tragedy of The Commons’ and the Analysis of the Elements Involved in using the Game Theory This is a dilemma that arises from the situation where many individuals who are acting independently and rationally, consult their self-interest. This is the issue of depleting shared resources which is limited even in the circumstances where it is clear that it not an interest. It is clear that the interest of the self is at centre, as opposed to the risk that is common to all the players. 5. An Explanation of the Phenotype and Monomorphic ESS-It cannot be successfully Invaded by Either Hawks or Doves. The adaptive dynamics is that mutations are small in evolution branching, in the generation of polymorphisms. This makes them stable. Simultaneous existence of the monomorphic ESS is a generic phenomenon which makes it stable. This makes the adaptive dynamics quite distinct but will integrate in the system theory. The concept of hawk dove brings the different mixes in population and the ESS exists when the Hawk and Dove fitness are said to be equal (Beckert 423). Works Cited Beckert, Jens. The International Encyclopedia of Economic Sociology. Washington: Routledge Publication, 2005. Print. Beech, Colin. The Grail and the Golem: The Sociology of Aleatory Artifacts. New York: Rensselaer Polytechnic Institute Publication, 2008. Print. Read More