204_summer_2009_lecture_25

204_summer_2009_lecture_25 - University of Toronto...

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University of Toronto Department of Economics ECO 204 Summer 2009 Sayed Ajaz Hussain Lecture 25 1 S. Ajaz Hussain. sayed.hussain@utoronto.ca
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Last Time ± Investors’ Preferences ± Risk aversion ± Asset Return ± Asset Risk ± Portfolio Return ± Portfolio Risk ± Optimal portfolio allocation S. Ajaz Hussain. sayed.hussain@utoronto.ca 2
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Today ± Representing games ± Solving simultaneous move games ² Iterated deletion of dominated strategies ² Nash equilibrium ² Pure Strategies ² Mixed Strategies ± Some interesting games ± Price Wars ± Solving sequential move games ² Sub Perfect Nash Equilibrium (SPNE) S. Ajaz Hussain. sayed.hussain@utoronto.ca 3
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(Simple) Game Theory: Setup ± “Players” ² Rational, non cooperative ± “Actions” ² Assume discrete set of possibly random actions ± “Play” ² Simultaneous move game ² Sequential move game ² Sequence of simultaneous move games ± “Payoffs” ² Players receive known payoffs from their and others’ actions ± “Common Knowledge” S. Ajaz Hussain. sayed.hussain@utoronto.ca 4 Examples? Examples? Counterexamples?
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Simultaneous Game: Payoff Matrix S. Ajaz Hussain sayed.hussain@utoronto.ca 5 Player 2 “Column” Players 2’s Action 1 Action 2 Player 1 “Row” Players 1’s Action 1 Payoffs Action 2 By convention, player 1 is the “row” player Players can have altogether different strategies Players can have any number of strategies
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Example: Airlines Pricing ± Consider US Air and Delta competing on T.O. NYC route ± Airlines choose prices simultaneously tomorrow morning ² “One shot game” ± Prices can be: Low ($99) Medium ($119) High ($139) ± Payoffs – profits per seat ‐‐‐ are common knowledge ± What price will each airline announce tomorrow morning? S. Ajaz Hussain. sayed.hussain@utoronto.ca 6 Where do prices and payoffs come from? We’ll see how in Nutrasweet (A) case
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US Air vs. Delta S. Ajaz Hussain sayed.hussain@utoronto.ca 7 US AIR Delta High Price Medium Price Low Price High Price 34, 38 15, 42 6, 32 Medium Price 42, 20 22, 22 10, 25 Low Price 35, 7 27, 9 18, 16
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Solving One Shot Simultaneous Games by Dominant/Dominated Strategies ± Remember: we’re doing a “what if” analysis before play ± Suppose a player identifies: ² One action that’s better than another action regardless of what the opponent does ² i.e. some action is dominant over another ² The “superior” action is “dominant” ² The “inferior” action is “dominated” ² What would this player do? ² What would happen next? ² When would this iterative process stop? S. Ajaz Hussain. sayed.hussain@utoronto.ca 8
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Dominant Strategies S. Ajaz Hussain sayed.hussain@utoronto.ca 9 US AIR Delta High Price Medium Price Low Price High Price 34, 38 15, 42 6, 32 Medium Price 42, 20 22, 22 10, 25 Low Price 35, 7 27, 9 18, 16
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Dominant Strategies: No Solution S. Ajaz Hussain sayed.hussain@utoronto.ca 10 US AIR Delta High
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This note was uploaded on 05/02/2011 for the course ECO 204 taught by Professor Hussein during the Fall '08 term at University of Toronto- Toronto.

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204_summer_2009_lecture_25 - University of Toronto...

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