13. Gaming Theory & Strategic decisions

Two computer firms, A and B, are planing to market network systems for office information management. Each firm can develop either a fast, high quality system (High) or a slower, low quality system (Low). Market research indicates the resulting profit to each for the alternative strategies given by the payoff matrix to the right. 1) If both firms make their decisions at the same time and follow a maximin (low risk) strategy, what will the outcome be? 2) Suppose both firms try to maximize profit, but that Firm A has a headstart in planing and can commit first. Now what will be the outcome? 3) What will be the outcome of Firm B has the start in planing and can commit first? 4) Getting a head-start costs money. [...] Which firm will spend more to speed up planing? How much will it spend? 5) The amount that firm B would then spend to move first...

1) High / High No matter what, each firm secures the highest minimum profit when using high quality as dominant strategy. 2) Firm A choose HIGH and then firm B choose LOW 3) Firm B chose HIGH and then firm A choose LOW 4) Firm A should spend the most to speed up planing. It would be willing to spend $15 (85-75) because that is the difference between the maximum profit and the second best profit. 5) 0 / because it is unwilling to outbid Firm A for the option of moving first.

Two major networks are competing for viewer ratings in the 8-9PM and 9-10PM slots on a given weeknight. Each has two shows to full this time period and is juggling its lineup. Each can chose to put its "bigger" show first or to place it second the 9-10PM slot. The combination of decisions leads to the payoff matrix to the right. 1) Find the Nash equilibrium / equilibria, assuming that both networks make their decisions at the same time. 2) If each network is risk averse and uses a maximin strategy, what will be the resulting equilibrium? 3) What will be the Nash equilibrium if N1 makes the selection first? 4) What will be the Nash equilibrium if N2 makes the selection first? 5) Suppose the network managers meet to coordinate schedules and N1 promises to schedule the bigger show in the first slot. Is this promise credible? What would be the likely outcome?

1) Nash at First / First 2) N1 = First / N2 = Second 3) Nash at First / First 4) Nash at First / First 5) Credible Because there is no incentive for N1 to change and N2 will respond by choosing the first slot. (Nash is First / First)

When is a maximin solution a more likely outcome than a Nash equilibrium? A maximin solution is a more likely than a Nash equilibrium when

1) Opponents act sub-optimal 2) Opponents may act irrationally

1) What is a tit-for tat strategy? A tit-for-tat strategy is a strategy 2) Why is it a rational strategy for the infinitely repeated prisoners dilemma? A tit-for-tat strategy of cooperation is rational in infinitely repeated games because

1) in which a player responds in kind to an opponent's previous play. 2) no final period exists when it is optimal to undercut one's opponent.

Consider a game in which the prisoner's dilemma is repeated ten times and both players are rational and fully informed. Is a tit-for-tat strategy optimal in this case? 1) If a game is repeated ten times, a tit-for-tat strategy of cooperation 2) Under what conditions would such a strategy be optimal? A tit-for tat strategy of cooperation would

1) is not optimal because cooperation will break down in the last period and therefore in all preceding periods. 2) be optimal if the game were played an unknown / infinite number of times.

What is a strategic move?

A commitment to reduce one's options.

In many oligopolistic industries, the same forms compete over a long period of time, setting prices and observing each others behavior repeatedly. Given the large number of repetitions, why don't collusive outcome results? collusive outcomes are difficult to sustain in repeated games because

All payoffs might not be known prior to competition

Which of the following is NOT an example of a game?

Choosing the amount of automobile liability insurance to purchase

Three contestants, A, B, and C, each have a balloon and a pistol. From fixed positions, they fire at each other's balloons. When a balloon is hit, its owner is out. When only one balloon remains, its owner is the winner of a $1,000 prize. At the outset, the players decide by lot the order in which they will fire, and each player can choose any remaining balloon as his target. Everyone knows that A is the best shot and always hits the target, that B hits the target with probability .9, and that C hits the target with probability 0.85. Which contestant has the highest probability of winning the $1,000?

Contestant C because each player shoots at the contestant who is the best shot. -- Each contestant wants to remove the contestant with the highest probability of success. By following this strategy, each improves his chance of winning the game. A targets B because, by removing B from the game, A's chance of winning becomes much greater. B's probability of success is greater than C's probability of success. C will target A because, if C targets B and hits B, then A will target C and win the game. B will follow a similar strategy, because if B targets C and hits C, then A will target B and will win the game. Therefore, both B and C increase their chance of winning by eliminating A first. Similarly, A increases his chance of winning by eliminating B first.

What is a maxmin strategy?

Maximin strategy maximizes the minimum gain that can be achieved.

Is a dominant strategy optimal?

Yes, a dominant strategy is optimal no matter what an opponent does.

What is a dominant strategy?

a rule or plan of action for playing a game that maximizes a player's expected payoff no matter what an opponent does.

What is an optimal strategy?

a rule or plan of action for playing a game that maximizes a player's expected payoff.

How can the development of of certain kind of reputation be a strategic move? Developing a reputation can be a strategic move because

an anticipated response from one player affects the actions and responses of other players.

How does a game's Nash equilibrium differ from a game's maximin solution? At the Nash equilibrium, players

are doing the best given the actions of their opponents, but at the maximin solution, players are not necessarily doing the best they can.

To get another player to adhere to a bargaining position, a player could use a strategic move to

commit to something unpleasent

Explain the meaning of a Nash equilibrium. A Nash equilibrium is a set of strategies such that each player is..? How does it differ from an equilibrium in dominant strategies? A Nash equilibrium

doing the best it can given the actions of its opponent is not necessarily an equilibrium in dominant strategies but an equilibrium in dominant strategies is a Nash equilibrium

A strategic move limits one's flexibility and yet gives one an advantage. Why? A strategic move limiting one's flexibility can give that player an advantage by

influencing the behavior of other players

What is the difference between a cooperative and a non-cooperative game? The difference between a cooperative and a non-cooperative is that Give an example of each: 1) Cooperative game is 2) Non-cooperative game is

negotiation and enforcement of binding contracts are not possible in a non-cooperative game but are possible in a cooperative game. 1) Cartel agreement / multi-party bargaining / Joint Venture 2) a rave to obtain a patent / price competition

Why is an equilibrium stable in dominant strategies? An equilibrium stable in dominant strategies because

neither player has an incentive to change their behavior.

What is meant by "first-mover advantage"? Give an example of a gaming situation with a first mover advantage. "First-mover advantage" is where the player that moves first An example of a gaming situation with a first-mover advantage is

receives the highest payoff. connect-4 / checkers / tic-tac-toe / chess