Two companies are engaged in Bertrand-like competition. they make the some product at the some cost equal to $1.00. the customer does not know the production costs of two companies and announces that it will buy the product from the compay offering the lower price. the two companies must make their price offers simultaneously and only one time. in a case of a tie, the customer will break the tie by tossing a coin. due to local laws the price must be divisible by 10 cents. that is, price can equal to $0.00,$0.10,$0.20......etc., but it cannot, for example, be $2.718. all of the above is common knowledge among the players.

how many equilibria dose this game have ? prove it.