Distributed Systems Part II Solution to Exercise Sheet 8 1 Selfish
نویسنده
چکیده
a) i. The best response strategies are A: cache only if nobody else does. (B1) B: cache if neither A nor D cache. (B2) C: cache unless A caches. (B3) D: cache if neither A nor B cache. (B4) Nash equilibrium. If we assume that A plays xA = 1 (A caches) the system can only be in a NE if xB = xC = xD = 0 due to (B1). Since for all B, C, and D it is the best response not to cache if A does, x = (1000) is an Nash equilibrium. If xA = 0 then (B3) implies xC = 1. If furthermore, xB = 1 it must hold that xD = 0 due to (B2). This does not conflict with (B4), and (0110) constitutes another NE. Last, if xB = 0 then (B2) implies xD = 1, which is also okay with (B4). Hence (0011) is also a NE. NE = {(1000), (0110), (0011)}
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