# 1 1 Lesson overview BA 592 Lesson II.6 Strategic Move Theory Chapter 10 Strategic Moves Lesson II.6 Strategic Move Theory Each Example Game Introduces.

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1 1 Lesson overview BA 592 Lesson II.6 Strategic Move Theory Chapter 10 Strategic Moves Lesson II.6 Strategic Move Theory Each Example Game Introduces some Game Theory Example 1: Unconditional Strategic MovesExample 1: Unconditional Strategic Moves Example 2: CredibilityExample 2: Credibility Example 3: Implicit PromisesExample 3: Implicit Promises Example 4: DelegationExample 4: Delegation Example 5: BrinksmanshipExample 5: Brinksmanship Example 6: Threats verses PromisesExample 6: Threats verses Promises Lesson II.7 Strategic Move Applications

2 2 BA 592 Lesson II.6 Strategic Move Theory A game specifies the choices or moves available to the players, the order, if any, of those moves, and the payoffs resulting from all logically possible combinations of all the players’ choices. Equilibrium outcomes are typically affected by changing any one of those features --- adding or removing available moves, changing the order or removing order an making a game simultaneous, or changing payoffs. Hence, each player has an incentive to manipulate the game specifications to produce an outcome more to his advantage. Strategic moves are devices to manipulate games. Example 1: Unconditional Strategic Moves

3 3 BA 592 Lesson II.6 Strategic Move Theory The simplest way to change a game is to move first. But, what does it mean to “move first”? First, your actions must be observable to the other player. Second, they must be irreversible. Example 1: Unconditional Strategic Moves

4 4 BA 592 Lesson I.3 Sequential Move Theory The Street Garden Game tree to the upper left has a unique rollback equilibrium, with only Nina and Talia contributing and getting payoff 3. Nina gets payoff 4 if she commits to not contributing, say by putting all her money into an alternative project. That removes Contribute from her available moves, and changes the rollback equilibrium of the tree on the lower left. Example 1: Unconditional Strategic Moves

5 5 BA 592 Lesson II.6 Strategic Move Theory Conditional strategic moves are another way for Player A to change a game with Player B. Declare in the first stage: “In the following game, If you choose X 1, I will choose Y 1 ; if you choose X 2, I will choose Y 2 ; …. In other words Player A can commit to a response rule. One requirement is Player A has to be physically able to wait to make his move at the second stage until he has observed what Player B has irreversibly done. Conditional strategic moves can deter Player B from making a certain move or can compel Player B to make a move. The actions taken by Player A can be negative threats or positive promises. Example 2: Conditional Strategic Moves

6 6 BA 592 Lesson II.6 Strategic Move Theory Parents constantly try to influence the behavior of their children by using threats and promises. And children know well that many of these threats and promises are not credible. Much bad behavior can escape the threatened punishment if the child sweetly promises not to do that again, even though the child’s promise itself may not be credible. Determine the decision tree where the Child decides whether to eat his vegetables. (It is a decision tree since there is only one player.) Then change that tree into a game tree where a Parent first might threaten a child “no dessert unless you finish your vegetables” then the Child decides whether to eat his vegetables. Example 2: Conditional Strategic Moves

7 7 BA 592 Lesson II.6 Strategic Move Theory Decision tree without parents: Example 2: Conditional Strategic Moves

8 8 BA 592 Lesson II.6 Strategic Move Theory “No dessert unless you finish your vegetables” tree: Example 2: Conditional Strategic Moves

9 9 BA 592 Lesson II.6 Strategic Move Theory Threats by Player A to deter or compel a move by Player B implicitly imply a promise if Player B as requested. The Parent’s explicit threat “no dessert unless you finish your vegetables” implicitly makes the promise “dessert if you finish your vegetables”. Likewise, the explicit promise “dessert if you finish your vegetables” implicitly makes the treat “no dessert unless you finish your vegetables”. Example 3: Implicit Promises or Threats

10 BA 592 Lesson II.6 Strategic Move Theory Whether to make a treat or promise explicit, and which can be left implicit, depends on whether the payoffs to Player A make the threat or the promise a best response. On the one hand, if a parent thinks deserts are good for their child, then “no dessert unless you finish your vegetables” needs to be an explicit threat, while the promise “dessert if you finish your vegetables” can be left unsaid. On the other hand, if a parent thinks deserts are bad for their child, then “dessert if you finish your vegetables” needs to be an explicit promise, while the treat “no dessert unless you finish your vegetables” can be left unsaid. Explicit threats and promises are needed when they are not in Player A’s best interests to carry out. That is, when the threat does mutual harm to both players, or when the promise harms A. Example 3: Implicit Promises or Threats

11 BA 592 Lesson II.6 Strategic Move Theory Suppose a Child gets -1 happiness from eating his vegetables and 0 from not eating. Determine the decision tree where a Child decides whether to eat his vegetables. (It is a decision tree since there is only one player.) Suppose, regardless of whether the Child eats his vegetables, he gets +2 additional happiness from eating dessert and 0 from not eating dessert. Suppose the Parent gets +2 happiness if the Child eats vegetables and 0 from not eating, and an additional +1 happiness if the child eats dessert and 0 from not eating. Hence, change the decision tree into a game tree where a Parent first might threaten a child “no dessert unless you finish your vegetables” then the Child decides whether to eat his vegetables. Example 3: Implicit Promises or Threats

12 BA 592 Lesson II.6 Strategic Move Theory Decision tree without parents: Example 3: Implicit Promises or Threats

13 BA 592 Lesson II.6 Strategic Move Theory “No dessert unless you finish your vegetables” tree. (Parent payoff is first, Child second.) Example 3: Implicit Promises or Threats

14 BA 592 Lesson II.6 Strategic Move Theory Partial rollback solution: If the Parent makes no threat, the offers Desert (which the Child eats) but the Child refuses vegetables. The Parent gets payoff 1. If the Child eats vegetables, the Parent offers Desert (which the Child eats). Thus the threat need not specify “dessert if you finish your vegetables”. Example 3: Implicit Promises or Threats

15 BA 592 Lesson II.6 Strategic Move Theory Threat subgame: The threat can take the form of removing the option of desert if the Child does not eat vegetables, as shown in the tree on the upper left. Or, the threat can reduce the Parent’s payoff (say, wimpy reputation looses 2 units) if the Child does not eat vegetables but does eat desert, as show in the tree on the lower left. In either case, the Parent gets 3. Example 3: Implicit Promises or Threats

16 BA 592 Lesson II.6 Strategic Move Theory Threats can be made credible if Player A turns over their execution to a third party. Of course, this only solves the problem for Player A if the third party can credibly carry out both the threat of punishment for non-compliance by Player B and the implied promise of non-punishment for compliance by Player B. On the one hand, if the third party prefers to punish Player B, then credibility is doubtful for the non-punishment for compliance by Player B. On the one hand, if the third party prefers to not punish Player B, then credibility is doubtful for the punishment for non-compliance by Player B. Example 4: Delegation

17 BA 592 Lesson II.6 Strategic Move Theory Trade friction between the U.S. and Japan creates an incentive for strategic moves. Suppose either country can Open or Close trade to the other countries imports. Example 4: Delegation

18 BA 592 Lesson II.6 Strategic Move Theory For the U.S., the best outcome is Open imports by both countries. Specifically, suppose the U.S. values Open imports to Japan at 1 (because U.S. producers gain), and the U.S. values Open imports from Japan at 2 (because U.S. consumers gain more than U.S. producers loose). For Japan, the best outcome is Open imports to the U.S. but Closed imports from the U.S.. Specifically, suppose Japan values Open imports to the U.S. at 2 (because Japanese producers gain), and Japan values Closed imports from the U.S. at 1 (because the Japanese producers’ gain is valued more highly by the Japanese government than the Japanese consumers’ loss). Discuss the possibilities and difficulties for strategic moves in that Trade Relations Game. Example 4: Delegation

19 BA 592 Lesson II.6 Strategic Move Theory The U.S. and Japanese strategies and payoffs define a normal form. The U.S. has a dominate strategy of Open imports, and Japan has a dominate strategy of Closed imports. That gives Japan payoff 3, which is the highest possible, but the U.S. gets 2. Hence, the U.S. has an incentive for a strategic move to cause both countries to Open imports. Example 4: Delegation

20 BA 592 Lesson II.6 Strategic Move Theory The U.S. cannot get to its preferred strategies of Open imports by both countries by an unconditional strategic move to Open imports since Japan would respond with its dominate strategy of Closed imports. Can the U.S. get its preferred position with the threat “We’ll Close imports if you Close imports”? If that conditional strategic move were credible, Japan’s payoffs from Open would be 2, and from closed would be 1, so they would choose Open, giving the U.S. its preferred outcome. Example 4: Delegation

21 BA 592 Lesson II.6 Strategic Move Theory The threat “we’ll Close imports if you Close imports” is hard to make credible since it is not in U.S. interests to Close imports if Japan has Closed imports. In fact, Closed imports for the U.S. is a dominated strategy. One possible solution is to delegate the U.S. response to Japan to the U.S. Commerce Department, which is a group that values only U.S. producers, and for which Closed imports is a dominate strategy. That makes the explicit threat “we’ll Close imports if you Close imports” credible, but it makes the implied promise “we’ll Open imports if you Open imports” less credible. Example 4: Delegation

22 BA 592 Lesson II.6 Strategic Move Theory Putting it all together, delegation alone does not make both the threat “we’ll Close imports if you Close imports” and the implied promise credible. A reputation for toughness of the U.S. may have to decrease U.S. payoffs enough to make Closed imports in the U.S. be the best response to Closed imports in Japan. Example 4: Delegation

23 BA 592 Lesson II.6 Strategic Move Theory Threats are sometimes too large to be credible. “We’ll refuse to defend you in the future if you Close imports” might be too big to make credible based on our incentive to have a tough reputation. One way to scale down the size of such a treat is to make it a risk but not a certainty: “We are less likely to defend you in the future if you Close imports”. Threatening with the risk of large mutually-harmful penalties is called brinksmanship. Example 5: Brinksmanship

24 BA 592 Lesson II.6 Strategic Move Theory The chance of things sliding out of control is also often used as a tool of brinkmanship, because it can provide credibility to an otherwise incredible threat. For example, Kennedy was not willing to start a nuclear war over the Cuban Missile Crisis, but he was willing to take actions that risked the accidental start of a nuclear war. If Kennedy had said “If you station your warheads in Cuba, we start a shooting war and exterminate human life on this planet” nobody would have believed him, but instead Kennedy ordered a naval quarantine.Cuban Missile Crisis Example 5: Brinksmanship

25 BA 592 Lesson II.6 Strategic Move Theory Until the crisis ended, there was a continual risk of the accidental outbreak of nuclear war. For example, when an unknown Soviet anti-aircraft battery commander shot down an American U-2 surveillance plane without authorization. With U.S. forces on high alert, this single, unauthorized action could have prompted an attack on the Cuban bases, which might have quickly escalated into nuclear exchanges. In summary, Kennedy's actions created an ongoing elevated risk of an accidental nuclear exchange, with the hope that the Soviets would back down from positioning missiles in Cuba in order to reduce the risk Kennedy had created.an American U-2 surveillance plane Example 5: Brinksmanship

26 BA 592 Lesson II.6 Strategic Move Theory Threats and Promises by Player A are both costly if they actually occur, but if they are successful in changing the beliefs, and so the behavior, of Player B, the threat need not be carried out but the promise must be carried out. This has two implications: First, promises should be kept to the minimum to cause the desired change while threats can be bigger than the minimum, so long as the threat does not become incredibly big “Do that again and I’ll kill you!”. Second, threats are cheaper to Player A than promises. Example 6: Threats verses Promises

27 BA 592 Lesson II.6 Strategic Move Theory Suppose a Child looses 1 happiness from studying so hard he gets a B average. Determine the decision tree where a Child decides whether to study to get a B average. (It is a decision tree since there is only one player.) Example 6: Threats verses Promises

28 BA 592 Lesson II.6 Strategic Move Theory Decision tree without parents: Example 6: Threats verses Promises

29 BA 592 Lesson II.6 Strategic Move Theory Suppose, regardless of whether the Child gets a B average, he would loose 2 happiness if he were grounded at home for a month, and he would get +2 additional happiness if given a new bike. Suppose the Parent would get +2 happiness if the Child gets a B average, the Parent would loose 1 happiness if he grounds the child, and the Parent would loose 1 happiness if the Parent gives the Child a new bike (That 1 happiness lost is the sum total of the Parents value of the child getting the bike minus the purchase price.) Hence, change the decision tree into a game tree and decide whether it is better for the parent to threaten or promise. Example 6: Threats verses Promises

30 BA 592 Lesson II.6 Strategic Move Theory “You’re grounded if you get less than a B average” threat tree: Example 6: Threats verses Promises Suppose the Parent manages to impose a cost of C units of happiness if he does not carry through on the threat. For any C > 0, partial rollback of the tree indicates that, if not threatened, the Child will not study, and the Parent earns payoff 0. (The Parent’s payoff number is the first one.)

31 BA 592 Lesson II.6 Strategic Move Theory “You’re grounded if you get less than a B average” threat tree: Example 6: Threats verses Promises For any C > 1, complete rollback of the tree indicates that the Child will study, and the Parent will not ground the child, and the Parent earns payoff 2. (The Parent’s payoff number is the first one.)

32 BA 592 Lesson II.6 Strategic Move Theory “You get a bike if you get a B average” promise tree: Example 6: Threats verses Promises Suppose the Parent manages to impose a cost of C units of happiness if he does not carry through on the promise. For any C > 0, partial rollback of the tree indicates that, if promised a bike, the Child will not study, and the Parent earns payoff 0. (The Parent’s payoff number is the first one.)

33 BA 592 Lesson II.6 Strategic Move Theory Example 6: Threats verses Promises For any C > 1, complete rollback of the tree indicates that the Child will study, and the Parent will give the bike to the child, and the Parent earns payoff 1. (The Parent’s payoff number is the first one.) “You get a bike if you get a B average” promise tree:

34 BA 592 Lesson II.6 Strategic Move Theory Example 6: Threats verses Promises Putting it all together, the threat “You’re grounded if you get less than a B average” earns the Parent payoff 2 (and the threat is not carried out in equilibrium), which is better for the Parent than the payoff 1 from the promise “You get a bike if you get a B average”, which is better for the Parent than the payoff 0 from not threatening and not promising.

35 End of Lesson II.6 BA 592 Game Theory BA 592 Lesson II.6 Strategic Move Theory

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