Intelligent Agents: Technology and Applications Game Theory and Multiagent Systems

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Intelligent Agents Technology and
ApplicationsGame Theory and Multi-agent Systems

• IST 597B
• Spring 2003
• John Yen

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Strict Dominance

• A Strategy

Strictly dominates another strategy
if
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Strict Dominance

• Repeat
• Remove all strategies (rows) of player A that are
  strictly dominated by another row.
  
• Remove all strategies of player B (columns) that
  are strictly dominated by another column.
  
• Until no more rows or columns to remove

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Problem 1

• Apply the strict dominance strategy to find the
  equilibrium point of the following game.
  
• Can you always find an equilibrium point for a
  zero-sum game using this strategy?
  
• Can you always find an equilibrium point for a
  non-zero game using this strategy?

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Why not?

• The equilibrium point considers each players
  choices at a particular strategy pairs (without
  considering other choices of the opponent). The
  strict dominance considers all strategies of the
  opponent.
• The equilibrium point is a balance point
  reached by the two players not necessarily an
  optimal point.
  

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An N-player Prisoners Dilemma

• Farmer
• Strategy Restricted production
• Strategy Full production
• If all adopts , price is higher,
  individually better
  
• If all adopts , price is lower, individually
  worse
  
• For a particular farmer, full production leads to
  higher profit (since price is assumed to be not
  affected by one player), regardless of the
  strategies of other players.
• Full production strictly dominates restricted
  production.

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What will the farmers do?

• Greedy initially, predict the strategies of other
  farmers, adapt if needed.
  
• Cant control the weather
• Maximize their productions
• Build houses
• Merge small farms to improve productivity
• Switch planting plan
• Form coalitions to control production and price

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Problem 2 How will farmers behave in the real
world?

• They learn from their experience (i.e., the game
  is repeated every year).

Farmers form a coalition.
Government regulates to set constraints on
price/production.
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(Static) Coalition Formation

• Given a set of agents A, a value v for each
  subsets of A, Find a coalition structure (i.e.,
  partition of A), such that the overall utility is
  maximized.
• Distribute the pay off to members of the
  coalition.

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Pareto-optimal payoff distribution

• No agent is better off in any other valid payoff
  distribution for the given coalition structure.

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Stable Coalition Configuration

• No agent has an incentive to leave its coalition
  due to its assigned payoff.
  
• Different characteristics and criterions of
  stability define different solution space for
  cooperative games.

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Nash Equilibrium
Strategies of player 1


Strategies of player 2

is a Nash Equilibrium if

Neither player has motivation to change
unilaterally from its strategy.
If all players are selfish and non-cooperating
they would eventually adopt strategies that form
a Nash Equilibrium.


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Prisons Dilemma
Prisoner 1
Temporal Repetion of the Prisoners Dilemma
Repeated trials and receive payoffs after each
trial.
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Non-zero Game
Jill
Ballet
Boxing
(-1, -1)
(2, 1)
Boxing
Jack
(1, 2)
(-1, -1)
Ballet
Disclosing strategy is beneficial.
what are the equilibrium point?
Multiple equilibrium points with different total
returns?