Handout 3_sol.pdf - September 27th 2019 Email...

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Econ 522: Law and Economics September 27 th , 2019 TA: Meng-Chien Su Email: [email protected] Office Hours: Thursday 10:00-12:00 Social Sciences 6439 Handout 3: Dynamic Games & Concepts in Property Law 1 Review Dynamic Games Previously in the lecture we briefly talked about static games. To find Nash equilibrium in static games, we draw the payoff matrix and find the mutual best responses. However, when one of the players moves first, it is not static but a dynamic game . Usually we represent the dynamic games using a “game tree”. Example: An example of an extensive form game is given by the following simple game tree. Root Node: Player 1 Decision Node: Player 2 Terminal Node (Payoff 1, Payoff 2) Action 2L Terminal Node (Payoff 1, Payoff 2) Action 2R Action 1L Terminal Node (Payoff 1, Payoff 2) Action 1R 1. Components Extensive Form Game: A strategic interaction in which moves may occur sequentially. Player: Participants in the game. Node: Point in the games. Edge: Directed connections between certain nodes. Tree: A set of nodes and directed edges connecting them. Decision Node: A node with outgoing edges. Root: The first node in the game tree. A decision node with only outgoing edges. Terminal Node: A node with only incoming edges. Action: Describes what occurs along a given edge. Payoff: The utility of each player defined at every terminal node. 2. Assumptions Common knowledge of rationality: Players are rational. All players know that all players are rational. All players know that all players know that all players are rational... Sequential rationality: Whatever happens first, players will continue to act rationally in their own best interest from the point onward. 1 Revised from Jonathan Becker’s discussion section handout in Fall 2018. 1
3. Solution Concepts Subgame: A portion of an extensive form game which starts from one of the decision nodes and includes all subsequent nodes. Subgame-Perfect Equilibrium (SPE): When an equilibrium satisfies sequential rationality, we call it Subgame Perfect. SPE require that all players play best-responses (Nash Equilibria) in each subgame. Backwards Induction: We find SPE by solving the extensive form game backwards i.e. from the bottom subgame. Optimal choices in the last subgame would determine the payoffs in the second- to-last subgames, which allow us to determine the optimal choices in the second-to-last subgames. Iteratively applying this procedure gets us to the SPE. Concepts in Property Law 1 ) Principles for Establishing Ownership First Possession: Property rights determined by order of arrival. Pro: Simple to determine who possessed property first. Easy to administer.

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