Sequentially Rational Nash Equilibrium in Bidding Games
What is the sequentially rational Nash equilibrium for the bidding game?
Considering the values and bid amounts of the bidders, what are the equilibrium bids?
Answer:
The sequentially rational Nash equilibrium bids for the bidding game are Bidder 1: $100, Bidder 2: $90, Bidder 3: $95.
Explanation: In the given scenario, the bidders have different valuations for the object they are bidding on and limited budgets to place their bids. To determine the sequentially rational Nash equilibrium, we need to analyze each bidder's situation.
Bidder 1 values the object at $120 but only has $100 to bid with. Given their budget constraint, Bidder 1's optimal bid would be $100, as they cannot afford to bid higher than that.
Moving on to Bidder 2, they value the object at $100 and have $90 to bid with. Bidder 2's best response would be to bid $90, which is their maximum bid amount.
Lastly, Bidder 3 values the object at $95 and has $120 to bid with. Bidder 3's optimal bid would be $95, as it aligns with their valuation of the object.
Therefore, the sequentially rational Nash equilibrium bids are as follows:
- Bidder 1: $100
- Bidder 2: $90
- Bidder 3: $95
These equilibrium bids ensure that each bidder's bid is the best response to the bids of the other bidders in the game, leading to a stable outcome.