International Politics POL UA 700 Professor Jenn Larson Class 5 February 11 2014 Game Theory and War as Bargaining Today s Agenda 1 Review Prisoner s Dilemma Chicken and Stag Hunt 2 Sequential Decisions and Credibility 3 Unpredictability 4 How to Think About War 5 War as Bargaining Review Understanding Outcomes Actors have interests and interact with other actors Understanding the outcomes of interactions can be di cult Game theory helps us study strategic interactions Classifying Outcomes in the Prisoner s Dilemma Partner C D C 3 3 0 4 You D 4 0 1 1 Nash Equilibrium Pareto E cient Nash Equilibrium no player has an incentive to change their strategy given the strategies chosen by others Pareto E cient no other outcome to the game would be better for one player without being worse for the other player s Sometimes some Pareto E cient outcomes are more desirable than others Welfare Maximizing no other outcome to the game produces a larger sum of all players payo s Classifying Outcomes in the Prisoner s Dilemma Partner C D C 3 3 0 4 You D 4 0 1 1 Nash Equilibrium Pareto E cient Welfare Maximizing Nash Equilibrium no player has an incentive to change their strategy given the strategies chosen by others Pareto E cient no other outcome to the game would be better for one player without being worse for the other player s Sometimes some Pareto E cient outcomes are more desirable than others Welfare Maximizing no other outcome to the game produces a larger sum of all players payo s Other strategic situations Chicken vs Stag Hunt vs Coordination Games C D C D C D C 0 0 1 1 C 3 3 0 2 C 3 2 0 0 D 1 1 3 3 D 2 0 1 1 D 0 0 2 3 Chicken Stag Hunt Coordination Nash Equilibrium Pareto E cient Welfare Maximizing Examples in IR Chicken DC CC CD DD Cuban missile crisis Stag Hunt CC DC DD CD Setting international standards Coordination CC DD CD DC Scienti c standard measurements What happens if we repeat the Prisoner s Dilemma Things like lack of trust lead to the security dilemma If both sides can commit to playing the PD inde nitely then there are more cooperative equilibria available This arises because repetition leads to Opportunities for reciprocity Opportunities for punishment Example retaliatory tari s in trade policy We ll see an example the repeated Prisoner s Dilemma when we read Fearon and Laitin 1996 How Can We Get Along Factors that facilitate cooperation Institutions state know they need to do business in the UN Information needed for knowing when to reciprocate punish Valuing the future More on this in week 5 Institutions can facilitate cooperation domestically on international issues as well as facilitate cooperation directly between countries Two More Issues 1 Credibility 2 Predictability A two step example Suppose the USSR must decide whether or not to attack a member of NATO If the USSR decides to attack NATO must decide whether to respond with conventional or nuclear weapons We can represent the possible payo s utilities with a tree A Sequential Move Game Conventional 1 1 NATO Attack Nuclear Soviets 100 100 StatusQuo 0 0 Payo s to USSR USA A Sequential Move Game NATO moves second The Soviets can gure out what NATO s best response would be Conventional 1 1 NATO Attack Nuclear Soviets 100 100 StatusQuo 0 0 Payo s to USSR USA A Sequential Move Game NATO moves second The Soviets can gure out what NATO s best response would be Conventional 1 1 NATO Attack Nuclear Soviets 100 100 StatusQuo 0 0 Payo s to USSR USA A Sequential Move Game NATO moves second The Soviets can gure out what NATO s best response would be Conventional 1 1 NATO Attack Nuclear Soviets 100 100 StatusQuo 0 0 Payo s to USSR USA The trick to avoiding an attack is to convince the Soviets that if they choose Attack NATO would choose Nuclear despite their best response of Conventional A Sequential Move Game The trick is to convince the Soviets that if they choose Attack NATO would choose Nuclear despite their best response of Conventional NATO Attack Nuclear Soviets 100 100 StatusQuo 0 0 Payo s to USSR USA A Sequential Move Game The trick is to convince the Soviets that if they choose Attack NATO would choose Nuclear despite their best response of Conventional NATO Attack Nuclear Soviets 100 100 StatusQuo 0 0 Payo s to USSR USA Must credibly convey a willingness to go nuclear Credibility How to credibly convey a willingness to go nuclear Tell the Soviets that the US will use nuclear weapons Establish a reputation for irrationality Burn the conventional forces The Role of Unpredictability Sometimes being unpredictable is the best strategy Odds 1 Finger 2 Fingers 1 Finger 1 1 1 1 Evens 2 Fingers 1 1 1 1 Let s play Unpredictability in IR If a rebellion can only attack some cities in a country and if a ruling power can only fortify some cities in a country uncertainty is key Wrapping up Game Theory Framework for simplifying and representing strategic environments Demonstrates how interactions can keep actors from getting what they want Sometimes the most desirable outcome cannot be obtained even when players play their best responses Highlights the problem of credibility Highlights the problem of predictability Let s turn to a particular strategic context war Clarifying Terms War Interstate War Civil War An event involving the organized use of military force by at least two parties that satis es some minimum threshold of severity A war in which the main participants are states A war in which the main participants are within the same state such as the government and a rebel group More on this in Week s 5 and 6 What Do States Want Out of War States ght over Territory Out of 155 wars over the last 3 centuries over half involved Sometimes territory contributes to the wealth of a state Iran s con icts over territory southern oil elds Territory can have military or strategic value Golan Heights on border between Israel and Syria Territory can have ethnic cultural or historical value Kashmir Policies Regime Type Some states policies harm the interests of other states Afghanistan support of Al Qaeda The composition of a country s government may be viewed as a threat to another country communist regimes during the Cold War Con icts of Interest States may have con icting interests regarding territory policies regime type etc Why do states sometimes resort to war to resolve these interests War is Costly The costs of war can be counted on a number of dimensions Loss of human life Wars among states in the 20th century led to 40 million