Several strategic settings can be modeled as a tournament, whereby the probability of winning a certain prize not only depends on how much effort you exert, but also on how much effort other participants in the tournament exert. For instance, wars between countries, or R&D competitions between different rms in order to develop a new product, not only depend on a participant's own effort, but on the effort put by its competitors. Let's analyze equilibrium behavior in these settings. Consider that the benet that rm 1 obtains from being the rst company to launch a new drug is $36 million. However, the probability of winning this R&D competition against its rival (i.e., being the first to launch the drug) is x1 xl+x2' which it increases with this firm's own expenditure on MD, 251, relative to total expenditure, x1 + x2. Intuitively, this suggests that, while spending more than its rival, i.e., x. 2' x2 , increases rm 1's chances of being the winner, the fact that x1 ) x2 does not guarantee that firm 1 will be the winner. That is, there is still some randomness as to which rm will be the rst to develop the new drug, e.g., a firm can spend more resources than its rival but be \"unlucky" because its laboratory exploits a few weeks before being able to develop the drug. For simplicity, assume that firms' expenditure cannot exceed 25, i.e., 3': E [0,25] .The cost is simply xi, so rm 1's prot function is 1r,(x1,x2):36[ 3" Jx, x1+x2 and there is an analogous prot flmction for country 2: 2 (rhxz) =36[ x2 13:, I] +x2 2(x,,x2)=36[ x2 13:, INF-\"2 You can easily check that these prot mctions are concave in a rm's own expenditure, i.e., 2 6 34%;!) x? in the rm's R&D, the rst million dollar is more protable than the 10'h million dollar, e.g., the innovation process is more exhausted. 3 0 for every rm i={l, 2} where fit . Intuitively, this indicates that, while prots increase a. Find each rm's best-response function. b. Find a symmetric Nash equilibrium, i.e., x: = x; = x"