How Game Theory Explains Putin's Aggression: Why Russia Might Invade Ukraine


we're going to be looking at how game theory might help us understand the current tension between Russia and the West over Ukraine and how it might even help us to find a solution to the current crisis so, we're going to split this blog into two parts first we're going to explain how the game theory and specifically the difference between single and repeated games might help us understand Russia's current aggression in Ukraine second, we're going to have a look at how a game theorist would go about resolving the current crisis all right before we get into the first bit of the blog a couple of disclaimers and assumptions first any game-theoretic formalization of real-life requires considering just a few of the many possible outcomes and is necessarily a simplification it's therefore very possible that this analysis will neglect some important aspects of the current crisis but this blog isn't intended as a complete rendering of what's happening in Ukraineinstead, game theory is a sort of useful heuristic or model for simplifying and understanding real life second, this blog will assume that states are indivisible self-interested actors essentially that Putin and Russia are the same thing so when Russia acts aggressively the expected utility of the action is the same for both of them basically, we're not going to split Russia and Putin or the west and their politicians into separate actors this assumption that states not their governments are the principal actors in geopolitics is known as state realism anyway, let's get into it so the two states we're going to consider are Russia and what we'll call the west which is basically Nato plus or minus a few states we decided not to use Nato because a NATO obviously comes with its own set of rules which make the whole thing a bit more complicated and b at least in some cases the west might include states that aren't part of Nato like Sweden or Ukraine and some Nato states like say a badly behaved Hungary might not be considered part of the west broadly Russia can pursue one of two strategies towards the west which we'll call s1 ands2 either they can be aggressive or the can maintain the status Quo now in reality there are actually arrange of possible strategies there were degrees of aggression ranging from misinformation campaigns to nuclear war but for the purposes of this blog, we'll just separate it into status quo andaggressionfor the moment we'll assume that continuing the status quo means no change in utility for either side utility by the way is just a fancy word for how good an actor considers anoutcomeif the outcome would be better than whatthey already had then the utility would-be positive if it's the same it'll be Zero and if it's worse it'll be negative in response to Russian aggression the west basically has two possible responses which we'll call r1 and r2appeasement and aggression again, in reality, there are a range of options here there are degrees of aggression and degrees of appeasement but we're going to keep things simple for now, appeasement means 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 Minski which gave Russian-backed separatists in Donbas a constitutional standing inUkrainewe'll call this outcome west concession in utility terms west concession involves a loss for the west which we'll call negative one and again 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 o1and o2Russia 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 11 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 Wedow ell at least superficially the answer looks to be r1 appeasement assuming the probability of o2 war is greater than 10percent then r1 has a higher expected utility than r2expected 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 r1 is just negative 1 for the west because the on outcome is west concession which therefore, has a probability of 1. the expected utility of r2 is just the probability of war multiplied by its utility we can ignore the possibility of status quo because that has a value ouzerias long as the probability of war is greater than ten percent this means Thatte expected utility of r2 will be lower than that of r1 so the west should choose r1so, game theory tells the west that the 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 ies2is 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 r1 which increases the expected utility for s2consider 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 as individual games which is why it's been so quick to achieve appeasement while Putin is rightly treating it as a repeated game which is why he's been encouraged to go further this is partly a reflection of the political reality Putin will be in power long enough so that he'll likely playlots of these games whereas most western leaders only have four-year terms sonly get to play a single game anyway the point is it's possible that the current conflict can only partially be explained by the fact that the west is mostly treating Russian aggression as an isolated game while Russia is playing a repeated game things do seem to be changing though it does look like western leaders are wising up to this and it looks like by demanding so much Russia has essentially made r1 too unpalatable making our two more likely anyway, so what does this game theory recommend here well the west has to do what it can to make s1 more appealing than s2 to Russia it can do this by increasing the probability of r2 by essentially making the possibility of aggression more plausible to put in which would decrease the expected utility of s2 for Russia Orit can do it by increasing the appeal ofs1essentially while we assigned the status Quo a utility value of zero for both sides in practice Russia probably doesn't see it like that the status Quo isn't going well for Russia Ukraine is tilting ever more westwards while Russia is slipping both economically andpoliticallygame theory would recommend that if we want to discourage Russia from choosings2 we should improve the appeal of s1anyway, what do you think is this a plausible way of analyzing the current conflict over Ukraine and if so what does it tell us let us know your thoughts in the comments down below.

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