“Analysis of strategic behavior in the centipede game”

GUIDELINE FOR ASSIGNMENT 2

Essay should be properly structured, straight to the point and addresses the key points highlighted in

the assignment question.

A sample layout of the essay is as follows;

[INTRODUCTION]

Figure 1.1 shows the diagram set-up of the centipede game .

-Key points to address:

1. Briefly elaborate what is meant by a sub-game and illustrate in the case of centipede game.

2. Illustrate in detail how the unique subgame perfect nash equiibrium is obtained via the

method of Backward Induction. Points to address includes

- what is a Nash Equilibrium

-How backward induction leads to a Sub-Game Nash Equilibrium at every sub-game / node.

Illustrate this clearly.

-How this method ultimately leads to the unique sub-game Nash Equilibrium ; i.e. player 1

defaulting at node 1 ( beginning of the game).

[BODY - 2nd Paragraph E.g. ]

-Explain the conclusion of the unique Sub-game Nash Equilibrium; i.e. conclusion suggest

that a rational agent ( rationality) suggest that the player should defect right at the

beginning of the game. How is this counterintuitive? i.e. suggest that in-fact irrationality may

lead to even better outcome.... Elaborate further your reasoning with the payout given in

figure 1.1.

[BODY - 3rd Paragraph E.g.]

- Build further from 2nd paragraph why one would expect the game not to end on the first

node; i.e. demonstrate from the results in figure 1,1, it is clear that both players will receive

higher payoff by playing further into the game at subsequent nodes; i.e. both continue the

game.

-You should also highlight that both players are assumed to have perfect information and

hence can figure out the potential payoff each receive by prolonging into the game at each

turn. So what is the implication of this ?

[BODY - 4th/ 5th Paragraph]

- You should build on theoretical concepts to further strengthen your conclusion in

paragraph 3. Key points that should be made include

- Difference between a game that is only played once vs Centipede Game that can be played

for an finite number of times ; i.e. n times. What is the implication of this? { i.e. co-operation

vs non-cooperation / the chance of retaliation at a later stage vs no chance of retaliation

against opponent's action}. How this theorectical understanding enable us to appreciate why

we expect the game to continue further before being ended instead of ending at the first

node .

- Expand your explanation to this point with further illustration that was already

demonstrated in class. E.g. how

1. one may arrive at a pure strategy of continuing the game at the very first node,

2. and how individuals actually end up playing mixed strategy in between the first and

last node of the game via assigning probability to the opponent's level of co-

operation....

3. how this probability strengthen as one plays further into the game at the initial

stages and the implication

4. how this probability weakens further towards the end of the node and its

implication.

[CONCLUSION]

5. How the above entire demonstration suggest that the game will not likely end at

the first node and also Yet not end on the last node.