Value-Rationalizability in Auction Bidding

In a symmetric first-price or second-price auction, a bidding strategy is characterized as value-rationalizable if it can be viewed as being realized at a Nash equilibrium under the specification of a non-negative and increasing value function. In an environment where the underlying probabilistic framework is common knowledge, we investigate conditions for value-rationalizability by examining the value functions, which are induced by a bidding strategy. The existence of value-rationalizable strategies with infinite large induced functions is established. We argue that an improper specification of the value function should be attributed to bounded rationality. We show that, under assumptions, strategies which are not value-rationalizable are sub-optimal responses. Finally, the degree of irrationality is assessed by measuring the deviation of the induced function from being a proper value function in terms of its sign and monotonicity. The findings are illustrated by different examples in the independent private value paradigm and the interdependent value setting.