A painting by famous painter Renoir is on sale in a first price auction . Bidders are A and B. The minimum bid is $ 1 billion , and bids must be made in minimum $ 100 million increments . If both bidders bid the same amount , the winning bidder is determined by drawing lots ( winning probability is 50 percent ) . Bidder A assesses the value of the painting at $ 1.4 billion , and bidder B assesses it as $ 1.2 billion . Create pay - off matrix in the range of $ 1 billion to $ 1.4 billion and resolve the game