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                  nature private information relevant to the relationship. As is typical in
                  information  economics,  we  refer  to  the  player  with  the  private
                  information  as  the  informed  player  informed  player  and  the  player
                  without the private information as the uninformed player.

                         • Critical to our analysis of these situations is the bargaining game
                  that determines the contract. We will refer to the contract proposer as the
                  principal and the player who receives the proposal as the agent. More-

                  principal over, we assume contracts are proposed on a take-it-or-leave-it
                  basis: The agent agent’s only choices are to accept or reject the contract
                  proposed by the principal. Rejection ends the relationship between the
                  players. A key assumption is that the principal is the uninformed player.

                  Models like this, in which the uninformed player proposes the contract,
                  are  referred  to  as  screening  models.  In  contrast,  were  the  informed
                  player  the  contract  screening  proposer,  we  would  have  a  type  of

                  signaling model.
                         • A contract can be seen as setting the rules of a secondary game to
                  be played by the principal and the agent.

                         Given this information structure, the two parties interact according to
                  some specified rules that constitute the extensive form of a game. In this
                  two-person game, the players must contract with each other to achieve some

                  desired  outcome.  In  particular,  there  is  no  ability  to  rely  on  some
                  exogenously fixed and anonymous market mechanism. Our focus will be on
                  instances  of  the  game  where  the  informed  player  can  potentially  benefit
                  from  his  informational  advantage  (e.g.,  perhaps  inducing  a  buyer  to  pay

                  more for a good than necessary because she fears the seller is high cost).
                  But,  because  the  informed  player  doesn’t  have  the  first  move—the
                  uninformed  player  gets  to  propose  the  contract—this  informational

                  advantage  is  not  absolute:  Through  her  design  of  the  contract,  the
                  uninformed  player  will  seek  to  offset  the  informed  player’s  inherent
                  advantage.
                         The Two-Type Screening Model

                         We  will  begin  to  formalize  these  ideas  in  as  simple  a  model  as
                  possible, namely the two-type model. In the two-type model, the state of
                  nature can take one of two-type model two possible values. As is common

                  in this literature, we will refer to the realized state of nature as the agent’s
                  type. Given that there are only two possible state, the agent can have one of
                  just two types.

                         Before  proceeding,  however,  we  need  to  emphasize  that  such
                  simplicity  in  modeling  is  not  without  cost.  The  two-type  model  is
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