allpayauction.hpp

// This file is part of the BCESolve library for games of incomplete
// information
// Copyright (C) 2022 Benjamin A. Brooks
// 
// BCESolve free software: you can redistribute it and/or modify it
// under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// 
// BCESolve is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// General Public License for more details.
// 
// You should have received a copy of the GNU General Public License
// along with this program.  If not, see
// <http://www.gnu.org/licenses/>.
// 
// Benjamin A. Brooks
// ben@benjaminbrooks.net
// Chicago, IL
 
// Header for all pay auction example.
// RJM 9-17-2015
 
#ifndef ALLPAYAUCTION_HPP
#define ALLPAYAUCTION_HPP
 
#include "bce.hpp"
#include "bceabstractgame.hpp"
#include "bcegame.hpp"
 
class AllPayAuction : public BCEAbstractGame {
 
public:
 
  AllPayAuction(int nv,int na):
    BCEAbstractGame(nv,na,1,3) 
  {}
 
  double prior (int state,const vector<int> & types) const {
    return 1.0/numStates;
  }
 
  double objective (int state,
            const vector<int> & actions,
            int obj) const {
  
    if (obj<2)
      {
    // obj is the player whose payoff we are returning
    
    double val = static_cast<double>(state)/(numStates-1.0);
    double ownBid = static_cast<double>(actions[obj])/(numActions[obj]-1.0);
    double otherBid = static_cast<double>(actions[1-obj])/(numActions[obj]-1.0);
 
    if (actions[obj]>actions[1-obj])
      return val-ownBid;
    else if (actions[obj]==actions[1-obj])
      return 0.5*(val-ownBid);
    else if (actions[obj] < actions[1-obj])
      return -ownBid;
 
      } // players' payoffs
    else if (obj==2)
      { 
    double b0 = static_cast<double>(actions[0])/(numActions[0]-1.0);
    double b1 = static_cast<double>(actions[1])/(numActions[1]-1.0);
    return b0 + b1;
      } // seller's revenue
    
    return 0.0;
  } // objective
 
};
 
#endif