Book contents
- Frontmatter
- Contents
- List of Figures and Tables
- Acknowledgments
- PART I THE MANY DESIGNS OF AMERICAN STATE LEGISLATURES
- PART II HOW DESIGN AFFECTS A LEGISLATURE'S FORM
- PART III HOW DESIGN AFFECTS A LEGISLATURE'S FUNCTION
- Appendix to Chapter 3
- Appendix to Chapter 4
- Appendix to Chapter 5
- Appendix to Chapter 6
- Appendix to Chapter 7
- References
- Index
Appendix to Chapter 6
Published online by Cambridge University Press: 06 January 2010
- Frontmatter
- Contents
- List of Figures and Tables
- Acknowledgments
- PART I THE MANY DESIGNS OF AMERICAN STATE LEGISLATURES
- PART II HOW DESIGN AFFECTS A LEGISLATURE'S FORM
- PART III HOW DESIGN AFFECTS A LEGISLATURE'S FUNCTION
- Appendix to Chapter 3
- Appendix to Chapter 4
- Appendix to Chapter 5
- Appendix to Chapter 6
- Appendix to Chapter 7
- References
- Index
Summary
TECHNICAL DETAILS OF BARGAINING GAMES
I begin by introducing the notation that I use to summarize the players and concepts in these games. I refer to the governor as PG and to the legislature as PL. An offer (XL, XG) would give the legislature XL of the dollar and leave the governor with the remainder. This XL can fall anywhere in the [0,1] interval, and the players may divide the dollar as finely as they like. Rounds of play are numbered as T = {0, 1, 2,…}. A player's level of patience, δ, can be thought of as a discount factor. Under the assumption that this discount factor remains constant from round to round, the present value at the beginning of the game to PL of an agreement in round t is given by XLδt.
The sequence of play begins with the legislature proposing some division of the dollar (XL, XG). PG then decides whether to accept or reject this bargain. If he or she rejects it, play moves into the second round, where PG makes a counteroffer of some other division (YL, YG) and PL chooses to take it or to begin another round of negotiations. A rejected offer becomes void and does not bind the next proposal to fall within any range. There is no limit on how long the process can continue. Since XL + XG = 1, an agreement in round t can be completely characterized by (XL, t).
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- Publisher: Cambridge University PressPrint publication year: 2004