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Terminal Games
Theoretical Subtitle
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A Simple Game
1: A>B>C2: B>C>A3: C>A>C
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Backwards Induction
1: A>B>C2: B>C>A3: C>A>C
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Backwards Induction
1: A>B>C2: B>C>A3: C>A>C
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Backwards Induction
1: A>B>C2: B>C>A3: C>A>C
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This doesn’t work so well if we have a cycle.
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Cyclical Game
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3’s Turn: 3 prefers a4
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7’s Turn: 7 prefers a1
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And so on… After 14 moves we return to our original state.
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However, an equilibrium does exist.
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General Idea
• By choosing the optimum shortest path through a strongly connected component and directing all other nodes inwards we can extend backwards induction through the cycles.
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The ‘Optimum Path’
• The Optimum Path is such that the player controlling final node in the cycle chooses its preferred destination.
• This player has no incentive to alter the path – maintaining Nash Equilibrium.
• We will use limited backwards induction to find the Optimum Path.
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The ‘Shortest Path’
• The Shortest Path ensures that no player controls enough nodes to change the route through the component.
• Any change by a member of the path will loop back to the path, creating a cycle.
• No player on the path will change, resulting in Nash Equilibrium.
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Hopefully the two projects are connected.
Have a good day.
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