Lecture 5BComplete Information Games

This lecture analyzes complete information games, before turning to a discussion of Home Depot.

Imperfect monitoring

If the actions of those paid to make decisions on your behalf are hidden from you, whether you retain them or not cannot directly depend on what they do.

This creates a situation of moral hazard, because you cannot directly reward them for following your instructions.

In that case their employment contract with you typically depends on signals that are correlated with their behavior.

These issues are taken up in depth in 45-976:Bargaining, Contracts and Strategic

Investment.

Investment broker

This game is neither a simultaneous move game, nor a perfect information game.

However the second mover, the client, knows more than the first mover, her broker.

For that reason, this is an example of a complete information game.

Strategic form of investment broker

The easiest way of solving this game is to directly analyze its strategic form.

The strategies for each player are shown in the matrix.

To obtain the payoffs suppose, for example, the broker chooses “tech” and the client’s strategy is “continue with broker”. Then the broker’s expected compensation is: 0.5*3 + 0.5*9 = 6

Solution to investment broker

This game is dominance solvable.

The broker should choose “tech” because it is a dominant strategy.

The investor should use the signal she receives about the economy, picking the strategy “continue if new, liquidate if bubble”.

Complete information games

Games where each player knows at least as much as everyone who has moved before him/her are called complete information games.

Complete information games include simultaneous move and perfect information games.

The solution to any complete information game is typically found by decomposing it into a sequence of solutions to smaller reduced games, and using the tools developed for perfect information games and simultaneous move games.

Read Chapter 11, “Complete Information Games” in Strategic Play.

Unrest down underCoal miners rank amongst the highest paid workers Australia, and the media are not shy about broadcasting this fact.

Encouraged by a conservative government, several years ago a major coal exporter in Australia began to negotiate with its workers individually.

In this way the exporter hoped to undermine the power of the union representing the workers, and ultimately reduce the miner’s wages by encouraging entry into that profession.

Industrial Dispute

This game can be solved by combining the dominance principle used in simultaneous move games and the roll back rule used in perfect information games.

Subgame for industrial dispute

Consider what would happen if management chose “Continue to de-unionize”.

Having reached the second choice node of the union, the remainder of the game could be considered a game in its own right.

This is why we call it a subgame.

In this case the subgame is itself a simultaneous move game.

The reduced game

Having solved the subgame, we now substitute its solution into the main game, to form a reduced game

Notice that this procedure mimics the roll back method we used to solve perfect information games.

Strategic form for industrial dispute

Other Nash equilibrium in this game

There are two other Nash equilibrium in this game, top right and bottom left, but both involve playing weakly dominated strategies.

Considering the top right cell, the union’s strategy of “go on strike, continue with strike” is an incredible threat to the employer, and is dominated by “go on strike, settle the dispute”.

Just in time

3/20*50+17/20*50=50

3/20*400-17/20*60=9

3/20*2+17/20*2=2

3/20*248-17/20*12=27

Reduced game for component supplier

Taking the expected value over the nodes that involve nature (and the possibility of breakdown), we obtain the reduced game depicted on the right.

Subgame for component supplier

Here we see that a subgame begins at the node reached by Pratt & Whitney choosing “Wait” and Boeing choosing “Wants part”.

The subgame is itself a perfect information game, and trivially solved by the choice “Make part”.

Strategic form for the reduced game

Folding the solution of the subgame into the extensive form, we see the resulting is a 2 by 2 simultaneous move game with the strategic form depicted.

Alliance

Strategic form of a subgame for Alliance

If GM does pursue a formal relationship with Hyundai, then it would enter a simultaneous move subgame in which each company determined its effort level informally.

The value of a formal relationship, incurring the costs of lawyers, is evident.

Solution to Alliance

In the subgame modeling an informal alliance, both players have a dominant strategy of exerting “minimal effort”.

The value of a formal relationship, incurring the costs of lawyers, becomes evident.

Background to Home Depot case

Games where each player knows at least as much as everyone who has moved before him/her are called complete information games.

Complete information games include simultaneous move and perfect information games.

The solution to any complete information game is found by decomposing it into a sequence of solutions to smaller reduced games, and using the tools developed for perfect information games and simultaneous move games.

Read Chapter 11, “Complete Information Games” in Strategic Play.

Who are the main playersin the Home Depot case?

Robert Nardelli, CEO of Home Depot.

Shareholders in Home Depot.

Shareholders in Lowe’s. (Note that Lowe’s are smaller than Home Depot.)

Board of directors of Home Depot

What can they do?

Robert Nardelli, can refashion Home Depot stores, for example orienting towards building contractors and away from homeowners.

The Board sets CEO compensation, and his term of office.

Shareholders in Home Depot can call for proxy votes to change the composition of the Board.

What do they they know?

Robert Nardelli knows where his strengths lie, and maybe able to hide his actions from the Board, at least initially.

The Board knows the plans of Nardelli, and is privy to early indicators of how successful his strategy is.

Shareholders see the financial results after the strategy has been implemented , along with those of Lowe’s.

How do the players evaluate the consequences?

Robert Nardelli cares about his compensation and future job opportunities.

Shareholders in Home Depot care about capital gains and dividends.

Shareholders in Lowe’s care about capital gains and dividends.

Board of directors of Home Depot can be voted in or out of office. Their networking opportunities help shape their financial portfolios and other lifestyle.

Home Depot in extensive form

There are several ways of reconstructing this business scenario.

One intriguing question is whether Nardelli could foresee the solution outcome at the beginning of the game or not?

Lecture summary

In games of complete information where there is more than one pure strategy equilibrium, we showed how to extend the roll back solution to find the solution, and showed why some of the other Nash equilibrium involve making threats that are not credible.