Following the outbreak of Covid-2030, two firms, Aand B, hereafter Firm A and Firm B respectively, are bidding for a government R&D contract. The lowest bid gets the contract (coin toss in the event of a tie). The government will not pay more than $5 billion and requires that bids are an integer between $2 billion to $5 billion The winner of the auction receives their bid to develop a vaccine for Covid-2030. The R&D cost is $2 billion which is the same for both firms.

Create the payoff matrix for this game. Are there any strictly-dominated strategies? Are there any weakly-dominated strategies? Find all the Nash equilibria.