# A Basic Framework

Game theory is the formal study of conflict and cooperation.^{8} In the context of the historical development and integration of the MR, Pham Do and Dinar (2014) argue that a negotiation process between upstream (China) and downstream (four LMB countries, represented by MRC) can be considered as a two-stage game. In the first stage, countries (China and LMB) can play at being non-cooperative over independent policy issues (strategies) such as energy (hydropower generation), trading, and the ecosystem (fishery and agriculture) to determine (evaluate) their policy (variables). Final outcomes, as the results of linked issues,^{[1]} are then considered in the second stage for negotiating nations.

Mathematically, let *N* = {1,2..., n} be a set of policy issues. Assume that the upstream (U) and downstream (L) simultaneously make a policy choice or action *aj=(a*_{n},... *aj _{n}) e A*j, where

*J=U, L;*and each action (policy) profile

*a*= (a

_{U},

*a*=

_{L})eA*A*

_{u}x

*A*

_{l}specifies a policy choice for each player (region) with respect to each

*i*e

*N*. Furthermore, for each issue

*i*e

*N*, each player

*j*has a measurable payoff function

*w‘J*on action profile

_{i}*a*with the objective function of players being linearly separable in policy issues; that is,

*wj =*The

_{1}w‘j_{i}^{[2]}corresponding stage game with strategy space *aj=A _{n}* x

*A*j

*.. .x*

_{2}*Aj*= {c,d}

_{n}^{n}is denoted by Г. For example, for policy profile

*a = (a*and two issues

_{U}, a_{D})*i*and

*k*(e.g., water and trading), the two-person games r,(a) and r

_{k}(a) can be described in the following two matrices:

Conflict or non-cooperative strategy refers to a situation in which a binding agreement cannot be achieved; while it is possible in cooperative strategy.

To achieve a basin-wide agreement through linked issues, each player can consider two possible actions: *C* (or c) for cooperating or *D* (or d) for defection (selfish policy action). For any two independent games, the values of a two- linked game are determined as the sum of two values in these games. Hence, in a linked game, player *J*s payoff is *wj **= **w^**j* + w^. The objective of each player is to maximize the final outcome *Wj **= **max _{a}*

*{*

*Wj*

*+*

_{i}*w‘J*

_{k}*}*(for further details, see Pham Do, Dinar, and McKinney 2012). Without loss of generality, it is assumed that both the LMB and China (UMB) are faced with two strategies— cooperation and non-cooperation—in each independent game.

- [1] The idea is that linking two (or more) policies (regimes) could allow countries to usesurplus enforcement power that may be available in one policy domain to discipline cooperationin other domains.
- [2] Such as dam construction plan, trading and energy plan, ecosystem protection, andenvironmental policy, and so on.