that the west will likely be forced into making some sort of concession that might involve for example russia taking de facto control of crimea or agreeing to minsk ii which gave russian-backed separatists in donbass a constitutional standing in ukraine we'll call this outcome west concession in utility terms west concession involves a loss for the west which we'll call negative one and a gain for russia which we'll call plus one aggression from the west is more uncertain there are basically two possible outcomes which we'll call oNUMBER_TOKEN and oNUMBER_TOKEN russia backs down or war russia backing down returns us to the status quo so we'll assign an expected utility of zero for both sides war however is the worst outcome for both sides so we'll assign it a utility value of negative NUMBER_TOKEN for both sides this gives us the following decision tree anyway what does game theory say that both actors should do here well let's look at it from the west's perspective first russia acts aggressively so what do we do well at least superficially the answer looks to be rNUMBER_TOKEN appeasement assuming the probability of oNUMBER_TOKEN war is greater than NUMBER_TOKEN percent then rNUMBER_TOKEN has a higher expected utility than rNUMBER_TOKEN expected utility is essentially calculated by taking the utility of various outcomes multiplying them by their respective probabilities and then adding them together the expected utility of rNUMBER_TOKEN is just negative NUMBER_TOKEN for the west because the only outcome is west concession which therefore has a probability of NUMBER_TOKEN. the expected utility of rNUMBER_TOKEN is just the probability of war multiplied by its utility we can ignore the possibility of status quo because that has a value of zero as long as the probability of war is greater than ten percent this means that the expected utility of rNUMBER_TOKEN will be lower than that of rNUMBER_TOKEN so the west should choose rNUMBER_TOKEN so game theory tells the west that they should go for appeasement or does it well it would if this was what's known as a one-off game i.e the game was only being played once in that case avoiding the possibility of war at the expense of some relatively minor concession is sensible but it's not this is a repeated game which makes things a lot more complicated because if the west chooses appeasement they make russian aggression in the future far more likely and russian aggression iesNUMBER_TOKEN is far worse for the west than the status quo this is because from russia's point of view if the west chooses appeasement this suggests that they're more likely to choose it again in the future this increases the probability of rNUMBER_TOKEN which increases the expected utility for sNUMBER_TOKEN consider an analogous real-life example if someone mugs you in the street the sensible thing to do is hand over your stuff it's not worth risking your life for an iphone however if that same mugger starts mugging you every monday then the optimum strategy changes and it becomes sensible to put up some sort of resistance i.e call the police this reaction wouldn't be sensible in an isolated mugging it makes it slightly more likely that you get stabbed the police are unlikely to retrieve your phone and you'd have to waste time filling out paperwork but if the same person was mugging you weakly then some sort of deterrence makes sense it's a similar thing here the west is apparently treating these skirmishes with russia
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