Game Theory Wireless and Communication Networks

Question: Discuss about theGame Theoryfor Wireless and Communication Networks. Answer: Part B The game is being played by two people James Dean and Buzz Gunderson. The first person is declared as chicken and the last person is a hero. The objective of two people is to get the favour of Judy. In order to play the game, they have to take life risk. The payoff matrix shows the outcome of each strategy taken by James and Buzz. If James chooses to be chicken, Buzz will choose to be rooster as will give higher payoff (50,100). The person jumps later from the car, will be the hero. If both of them choose to get out of the car at the same time, they will get the equal payoff of (70, 70). If nobody comes out of the car, both of them will be loser to get (0,0) and life will be in danger. A strategy is become dominant, when a player chooses a strategy every time, irrespective of what the opponent chooses. A player has always the highest payoff or utility from the dominant strategy compared to any other strategy (Myerson 2013). At the start of the game, both think to be a hero in order to get favour of Judy and to get the highest payoff of 100. If James chooses to be chicken, he is better off if Buzz is also choosing chicken. If James chooses to be rooster, his payoff will be the maximum if Buzz chooses to be chicken. Chicken is the dominant strategy for both the player as (70, 70) is the optimum strategy for both of them. This is the weakly dominant strategy as for other options, there is risk of losing. (70, 70) is as good as any other strategy. This strategy is not strictly dominant; there is an internal desire of being a hero making the opponent fool. (50,100) and (100, 50) are therefore dominated strategy. Buzz Chicken Rooster James Chicken 70 , 70 50 , 100 Rooster 100 , 50 0 , 0 The above payoff matrix shows the outcome of different strategies. As (70, 70) is the dominant strategy, other strategies are dominated strategy. Choosing Rooster is the dominated strategy for both James and Buzz. As (70, 70) is the dominant strategy for both of them, Buzz assumes that James never plays Rooster and the Buzz also thinks the same. Therefore, from the view point of James, the payoff matrix will be Buzz Chicken Rooster James Chicken 70 , 70 50 , 100 James also thinks that Buzz will never wish to become rooster, as there is life risk. The payoff matrix from the view point of Bazz is Buzz Chicken James Chicken 70 , 70 Rooster 100 , 50 Given opponents expected payoff, both are likely to maximise their own payoff, which is at least as good as other payoffs. Hence, both are likely to choose to be a chiken and will end up to (70, 70) outcome. This is the outcome in the elimination process of dominance. As there is a life risk and both James and Buzz feel the endangered at the same time, they choose to be the chicken before plunge to the rocks. Hence, the optimum outcome would be (70, 70). This is the weak dominance strategy. If James chooses chicken, there is a fear that Buzz may choose rooster. As there is no negotiation between them, everyone thinks about the worst situation of getting nothing. Hence, both want to minimise their risks. Therefore, (70, 70) is the optimum strategy for both James and Buzz. This is the pure strategy Nash equilibrium of this game as this more likely to happen compared to other strategy. The game is played through maxi-min strategy. Everybody wants to maximise the payoff among the minimum as the payoff matrix is the combination of both good and bad outcome. In the view of Colman (2014), this is the low risk strategy. The logic behind this game is to get something instead of nothing. Therefore, the minimum expected payoff from both the player is the optimum outcome as the game strategy is risk reduction. In this game, it is better to save life instead of getting favour of Judy. One-Shot Simultaneous Game Firm 1 has three options, while firm2 has only two options. There is no dominant strategy for any of the firm. From the view point of firm 1, it chooses offer discount if firm2 chooses advertising campaign. If firm2 does nothing, advertising campaign is the optimal strategy for firm1. Now, from the view point of firm2, it chooses advertising campaign if firm1 does advertising or offer discount. However, its strategy changes if firm 1 does nothing. Doing nothing would give firm2 the higher payoff. No firm has strictly dominant strategy. Do nothing is the dominated strategy for firm1. The dominated strategy for firm1 is (0,0) and (3,5). Do nothing is the dominated matrix of firm2. For both the firms, this is the weakly dominated strategy as no one has strongly dominant strategy. The payoff matrix of by dominance is Firm 2 Advertising campaign Firm 1 Advertising campaign 1,2 Offer discounts 2,2 Firm2 has only option of advertising campaign, while firm1 has two options such as advertising and offer discounting. Given this framework, firm1 chooses offer discount to maximise its payoff. Hence, (2, 2) is the equilibrium outcome by dominance. If firm2 chooses advertising campaign, firm1 tries to maximise its outcome by choosing offer discount. If firm2 chooses do nothing, firm1 chooses advertising. When, firm1 chooses advertising or offer discount, firm2 chooses advertising. When firm1 chooses do nothing, firm2 will do nothing. The pure strategy Nash equilibria are (2, 2), (4, 1) (1, 2), (3, 5). Outcomes in (a) and (c) differs as the first one is based on pure Nash equilibrium strategy. The second one is based on the elimination of dominated strategy. Two methods are different. In the first case, the player considers all the strategy of the opponents and plays the game. In the second case, the dominated strategy is completely ignored by the player. Financial Literacy Summary of the Video The central idea of the video is risk diversification. It has been argued that people should not investment all the money in a single stock of a company or in a single share. If the company loses for any financial crisis or downfall in business, all the shareholders lose at the same time as they share both the profit and loss. Hence, the right way to diversify the risk is to put the savings in a portfolio, which consists of both risk free and risky assets and shares of different companies (Dresher, Shapley and Tucker 2016). It has been argued that investment in human capital, education is necessary to have a better life in future. However, more saving and less spending has negative effect on the economy in short run (Aumann and Brandenburger 2016). This is termed as paradox of thrift. Hence, people need to balance between saving and investment and need to choose right investment strategy to shape their life. The interesting topic in this video is paradox of thrift. As per general saving investment theory in long run, all savings are assumed to be invested. However, in much economy in Europe, it has seen that GDP has fallen despite having high saving rate (Han 2012). When people save more, they reduce their consumption expenditure. Therefore, aggregate demand falls in the economy. Excess supply creates in the market in the short run and hence, aggregate supply reduces and investment in the economy falls. Therefore, it is argued that excessive saving is not beneficial for the economy. Is paradox of thrift can sustain in long run? References Myerson, R.B., 2013.Game theory. Harvard university press. Colman, A.M., 2014.Game theory and experimental games: The study of strategic interaction(Vol. 4). Elsevier. Dresher, M., Shapley, L.S. and Tucker, A.W. eds., 2016.Advances in Game Theory.(AM-52)(Vol. 52). Princeton University Press. Han, Z., 2012.Game theory in wireless and communication networks: theory, models, and applications. Cambridge University Press. Aumann, R.J. and Brandenburger, A., 2016. Epistemic conditions for Nash equilibrium. InReadings in Formal Epistemology(pp. 863-894). Springer International Publishing.