Game theory is the study of strategic decision making between interdependent parties. The document discusses game theory concepts like pure strategies, payoffs, and the Prisoner's Dilemma. It then applies these concepts to analyze a scenario from the Batman movie where the Joker has rigged two boats to explode unless one boat detonates the other first. The analysis shows how assumptions in the basic Prisoner's Dilemma payoff matrix are oversimplified for this complex real-world scenario.

1. Submitted by
Allen Meshach
Game Theory
Archana Yadav
Ashwin John Oommen
Edison P. K
George T. Cherian

2. WHAT IS GAME THEORY?
• In strategic games, agents choose strategies that will
maximize their return, given the strategies the other
agents choose.
• The mathematics of human interactions
• Assumptions:
• The winner takes all, at the expense of the other player.
• Game theory further assumes the two players are
rational actors
• Each is trying to maximize his gain or minimize his loss.
• All payoffs are a gain for one player and a loss for the
other player.

3. APPLICATIONS OF GAME THEORY
• Mathematics • Psychology
• Computer Science • Law
• Biology • Military Strategy
• Economics • Management
• Political Science • Sports
• International Relations • Game Playing
• Philosophy

4. KEY ELEMENTS OF A GAME
• Players: Who is interacting?
• Strategies: What are their options?
• Payoffs: What are their incentives?
• Information: What do they know?
• Rationality: How do they think?

5. PURE STRATEGIES
• The upper value of the game is equal to the minimum
of the maximum values in the columns.
• The lower value of the game is equal to the maximum
of the minimum values in the rows.

6. PRISONER’S DILEMMA
• Two suspects arrested for a crime
• Prisoners decide whether to confess or not to
confess
• If both confess, both sentenced to 3 months of jail
• If both do not confess, then both will be sentenced
to 1 month of jail
• If one confesses and the other does not, then the
confessor gets freed (0 months of jail) and the non-
confessor sentenced to 9 months of jail
• What should each prisoner do?

7. PRISONER’S DILEMMA

8. Game Theory In
BATMAN ?

9. STORY LINE
• The Joker has rigged two ferries carrying people
out of Gotham to explode.
• One ferry carries mostly civilians with a
substantial National Guard presence.
• The other ferry contains large numbers of prison
inmates and some guards.
• The Joker has rigged both to explode, and he has
given the crew on each boat the detonators.
• Only they have the detonator for the other boat.

10. CONTD …
He announces the rules of the game to the crew
and passengers of each vessel-
• Each of them have the power to blow up the other
boat and then their boat will live.
• If they get to midnight with know no exploded
boats, the Joker will detonate both.
• Any attempt to defuse the bombs will result in
the destruction of both boats.

11. SOLUTION….??

12. • Clearly, the Joker's intention with this scheme was to
have one of the boats blow up the other
• The boat filled with criminals could easily overpower the
guards and blow up the boat of civilians to save
themselves.
• The tricky part for the people on both boats is to try and
guess what the other party is likely to do.
• The longer you wait, the more likely the scheme will be
foiled and both will be saved.
• On the other hand, the longer you wait the more likely the
other boat will decide to kill you.

13. Payoff Matrix - Simple Case
Prisoner Boat
Press Button Don’t Press Button
Civilian Boat Press Button Not Allowed ……. Dead
Don’t Press Button Dead....... DeadDead

14. ASSUMPTIONS
 No consequences -- social or otherwise.
 The probability of rescue before midnight is zero.
 The option of both pressing the button is not
allowed because presumably the blown up boat
would not have that option.

15. BEST OPTION
The situation described in the simple matrix will end:
Both sets of passengers would be running to push the
button.

16. Payoff Matrix - Complex Case
Prisoner Boat
Press Button Don’t Press Button
Civilian Boat Press Button Not Allowed Murderers Dead
Don’t Press Button Dead Murderers DeadDead
(Possibility of rescue)

17. PROBLEMS IN SIMPLE CASE
 There would very likely be consequences to blowing up the other boat.
 For the civilian boat, there is the social stigma of being murderers -- even if
it is murder of felons.
 For the prisoner boat, the social stigma may be less , but the legal
consequences are probably greater.
 Thus, in pressing the button, both actors face a non-zero penalty.
 The penalty is trivial compared to being dead, but it is still there.

18. PROBLEMS IN SIMPLE CASE (CONTD…)
 This being a superhero movie there is a non-trivial probability that the
people on both boats will be saved before midnight.
 The non-trivial possibility that both boats could live is a strong
temptation to wait and not push the button.
 The presence of these two complexities explains why this situation
doesn't immediately degenerate into explosion.
 The interesting part of game theory problems is that people vary in
their estimation of probabilities of other people's actions and vary in
their weighting of the different payoffs.
 This variation makes profit-maximizing play even more difficult to engineer.

19. Thank You…!!