Principles of Economics: Seminar 1 - Game Theory

Transcription

1 Principles of Economics: Seminar 1 - Game Theory July 18, 2017 Principles of Economics: Seminar 1 - Game Theory July 18, / 20

2 What is a game? Definition: A game is any situation involving two or more players in which the fate of each player depends not only on her actions but also on the actions of the other players. Principles of Economics: Seminar 1 - Game Theory July 18, / 20

3 What is a game? Definition: A game is any situation involving two or more players in which the fate of each player depends not only on her actions but also on the actions of the other players. Notes: 1 A situation can be economic, social or political, etc. 2 A player can be a person or a group such as a firm, a political party, a school, a country etc. 3 The fate of a player is what she cares about such as profit, happiness, winning an election, growth, money etc. 4 An action is a choice or a strategy. Principles of Economics: Seminar 1 - Game Theory July 18, / 20

4 Main ingredients According to the previous definition the main ingredients/components of a game are: 1 The players 2 The strategies available to them 3 Their payoffs Principles of Economics: Seminar 1 - Game Theory July 18, / 20

5 Main ingredients According to the previous definition the main ingredients/components of a game are: 1 The players 2 The strategies available to them 3 Their payoffs I would say that we need to add a fourth: 4 What information do the players have? What do they know? Principles of Economics: Seminar 1 - Game Theory July 18, / 20

6 Example 1 Big John and Little John eat coconuts, which dangle from a lofty branch of a palm tree. Their favorite coconut palm produces only one fruit per tree. To get the coconut, at least one of them must climb the tree and knock the coconut loose so that it falls to the ground. Careful energy measurements show that a coconut is worth 10 Kc (kilocalories) of energy, the cost of running up the tree, shaking the coconut loose, and running back down to the ground costs 2 Kc for Big John, but is negligible for Little John, who is much smaller. Principles of Economics: Seminar 1 - Game Theory July 18, / 20

7 Example 1 Moreover, if both individuals climb the tree, shake the coconut loose, then climb down the tree and eat the coconut, Big John gets 7 Kc and Little John gets only 3 Kc, because Big John hogs most of it; if only Big John climbs the tree, while Little John waits on the ground for the coconut to fall, Big John gets 6 Kc and Little John gets 4 Kc (Little John eats some before Big John gets back down from the tree); if only Little John climbs the tree, Big John gets 9 Kc and Little John gets 1 Kc (most of the food is gone by the time Little John gets there). Principles of Economics: Seminar 1 - Game Theory July 18, / 20

8 Example 1 Who are the players? What strategies/actions can they take? What are the consequences of each action? (Payoffs?) Principles of Economics: Seminar 1 - Game Theory July 18, / 20

9 Example 2 Advanced Micro Devices (AMD) has slashed prices of its desktop and mobile Athlon processors just days after a similar move by rival Intel. We re going to do what it takes to stay competitive on prices, said an AMD representative. [...] AMD s aggressive price-chopping means the company doesn t want to give up market share gains, even at the cost of losses on the bottom line, analysts said. (CNet News.com, May 30, 2002.) Principles of Economics: Seminar 1 - Game Theory July 18, / 20

10 Example 2 Who are the players? What strategies/actions can they take? What are the consequences of each action? (Payoffs?) Principles of Economics: Seminar 1 - Game Theory July 18, / 20

11 Example 2 In this example, the companies compete on price in order to gain market share. As a result of price cuts, during the first quarter of 2002, AMD increased processor shipments from the fourth quarter of 2001, topping 8 million, but processor revenue declined by 3%. In effect, the company sold more chips for less money than in the fourth quarter. Competing companies who go into such price wars do rarely, if ever, benefit from such competition. Principles of Economics: Seminar 1 - Game Theory July 18, / 20

12 Example 2: Is the outcome of a game always efficient? Clearly, rather than engaging in mutual price cuts, both Intel and AMD would have done better if they kept their prices higher. Cutting prices slightly might increase the overall market potential, i.e., the pie might get bigger. But decreasing the prices beyond a certain limit has a diminishing impact on the market potential. Hence, eventually the size of the pie does not increase anymore and firms have to fight even harder to get a bigger portion of the pie by slashing prices, and profits. Why do firms behave this way? In this situation, and in many others, firms are caught in what is known as the prisoner s dilemma. Principles of Economics: Seminar 1 - Game Theory July 18, / 20

13 Type of games Simultaneous move or sequential move Complete information or incomplete information One-shot game or repeated game Cooperative or non-cooperative Any combination of the above Principles of Economics: Seminar 1 - Game Theory July 18, / 20

14 Simultaneous vs sequential move In example 1 we have a simultaneous move game if both Big John and Little John have to decide their action at the same time. For example, if Big John has to decide first, and then Little John chooses an action observing what Big John did, then we have a sequential move game. Principles of Economics: Seminar 1 - Game Theory July 18, / 20

15 Complete vs incomplete information In example 1 we have a game of complete information if both Big John and Little John know their own payoff and also the payoff of the other player. For example, if Big John does not know the payoffs for Little John under the different actions then we have incomplete information. Principles of Economics: Seminar 1 - Game Theory July 18, / 20

16 One-shot vs repeated If players play the game only once, we have a one-shot game, if not we call it a repeated game (it can be repeated a finite number of times or infinitely many times) Principles of Economics: Seminar 1 - Game Theory July 18, / 20

17 Cooperative vs non-cooperative In non-cooperative game theory, we focus on the individual players strategies and their influence on payoffs, and try to predict what strategies players will choose (equilibrium concept). In cooperative game theory, we abstract from individual players strategies and instead focus on the coalition players may form. We assume each coalition may attain some payoffs, and then we try to predict which coalitions will form (and hence the payoffs agents obtain). Principles of Economics: Seminar 1 - Game Theory July 18, / 20

18 How can we solve a game? A central assumption in many variants of game theory is that the players are rational. A rational player is one who always chooses an action which gives the outcome he most prefers, given what he expects his opponents to do. The goal of game-theoretic analysis in these branches, then, is to predict how the game will be played by rational players, or, relatedly, to give advice on how best to play the game against opponents who are rational. Principles of Economics: Seminar 1 - Game Theory July 18, / 20

19 Prisoner s dilemma Can we solve the Prisonner s dilemma taking the following into account: A rational player is one who always chooses an action which gives the outcome he most prefers, given what he expects his opponents to do. Principles of Economics: Seminar 1 - Game Theory July 18, / 20

20 Prisoner s dilemma Can we solve the Prisonner s dilemma taking the following into account: A rational player is one who always chooses an action which gives the outcome he most prefers, given what he expects his opponents to do. Here both players have a dominant strategy. A strategy is dominant if, regardless of what any other players do, the strategy earns a player a larger payoff than any other. Principles of Economics: Seminar 1 - Game Theory July 18, / 20

21 Quality choice Suppose player I is an internet service provider and player II a potential customer. They consider entering into a contract of service provision for a period of time. The provider can, for himself, decide between two levels of quality 10 of service, High or Low. Principles of Economics: Seminar 1 - Game Theory July 18, / 20

22 Quality choice Suppose player I is an internet service provider and player II a potential customer. They consider entering into a contract of service provision for a period of time. The provider can, for himself, decide between two levels of quality 10 of service, High or Low. High-quality service is more costly to provide, and some of the cost is independent of whether the contract is signed or not. The level of service cannot be put verifiably into the contract. High-quality service is more valuable than low-quality service to the customer, in fact so much so that the customer would prefer not to buy the service if she knew that the quality was low. Her choices are to buy or not to buy the service. Principles of Economics: Seminar 1 - Game Theory July 18, / 20

23 Quality choice Principles of Economics: Seminar 1 - Game Theory July 18, / 20

24 Quality choice Here only one players has a dominant strategy. We can solve the game, or find the equilibrium if we eliminate the strategies that are dominated, because we know a rational player will never play them. Principles of Economics: Seminar 1 - Game Theory July 18, / 20

25 Quality choice Here only one players has a dominant strategy. We can solve the game, or find the equilibrium if we eliminate the strategies that are dominated, because we know a rational player will never play them. This is known as iterative elimination of strictly dominated strategies. Principles of Economics: Seminar 1 - Game Theory July 18, / 20

26 References Public/GTE%20Game%20Theory%20Basic%20Concepts.pdf games/cooperative_game_theory.pdf Principles of Economics: Seminar 1 - Game Theory July 18, / 20