valuation and payments in the utility expression of an agent are related linearly, i.e,
() = v
) - p
There is a common prior distribution of agent's preferences , where =
× ....... ×
. An individual belief function is derived from for each agent, given her
preference. The key assumptions in mechanism design are rationality and intelligence of
participating agents. The rationality assumption makes an agent to strategise only for its
own objectives. An agent is intelligent if she can make inference about the game induced
in the mechanism that a game theorist can make by knowing everything a game theorist
. . .
(.) . . . u
(.) are assumed to be common knowledge.
Properties of mechanisms
Some properties of mechanisms in quasi-linear environment are the following.
1. Allocative Efficiency (AE) - An efficient (or) optimal allocation a
total value of all the agents.
() = arg max
A mechanism is allocatively efficient if the allocation of the resource to agents is
2. Dominant Strategy Incentive Compatible (DSIC) - The mechanism is DSIC if it
incentivise agents such that truth revelation becomes dominant strategy of all the
valuation and payments in the utility expression of an agent are related linearly, i.e, u i () = v i (a i ; , 1 , 2 . a () = arg max aA iN v i (a i , i ).