# Modeling factions for ‘effects based operations’, part II: behavioral game theory

## Abstract

Military, diplomatic, and intelligence analysts are increasingly interested in having a valid system of models that span the social sciences and interoperate so that one can determine the effects that may arise from alternative operations (courses of action) in different lands. Part I of this article concentrated on internal validity of the components of such a synthetic framework—a world diplomacy game as well as the agent architecture for modeling leaders and followers in different conflicts. But how valid are such model collections once they are integrated together and used out-of-sample (see Sect. 1)? Section 2 compares these realistic, descriptive agents to normative rational actor theory and offers equilibria insights for conflict games. Sections 3 and 4 offer two real world cases (Iraq and SE Asia) where the agent models are subjected to validity tests and an effects based operations (EBO, as in Smith, Effects based operations: applying network-centric warfare in peace, crisis, and war, 2002) experiment is then run for each case. We conclude by arguing that substantial effort on game realism, best-of-breed social science models, and agent validation efforts is essential if analytic experiments are to effectively explore conflicts and alternative ways to influence outcomes. Such efforts are likely to improve behavioral game theory as well.

## Keywords

Political simulation Agent-based models Game theory Validation Policy analysis tools## Abbreviations

*S*2Pertains to dyadic scenarios, can be considered a simplified subgame in a triadic interaction. Dyadic scenarios are described without

*S*2 prefix*S*3Pertains to triadic scenarios

*S*3.1,*S*3.2,…,*S*3.6Each one is a triadic scenario

*S*2*x*[*FxFy*]Payoff to

*x*in a dyadic scenario, when Both*x*and*y*are fighting. Mutual conflict*S*2*x*[*FxCy*]Payoff to

*x*in a dyadic scenario, when*x*is fighting while*y*has compromised*S*2*x*[*CxFy*]Payoff to

*x*in a dyadic scenario, when*y*is fighting while*x*has compromised*S*2*x*[*CxCy*]Payoff to

*x*in a dyadic scenario, when both*x*and*y*have compromised. Mutual compromise*S*3*x*[*FxFy*,*FxFz*,*FyFz*]Payoff to

*x*in a triadic scenario, when*x*,*y*and*z*are fighting with each other. Mutual conflict*S*3*x*[*CxFy*,*CxFz*,*CyCz*]Payoff to

*x*in a triadic scenario, when the aggressors*y*and*z*independently attack a passive*x**S*3*x*[*CxCy*,*CxFz*,*CyFz*]Payoff to

*x*in a triadic scenario, when*z*attacks coalition of*x*and*y*, who do not fight back*S*3*x*[*CxCy*,*FxFz*,*FyFz*]Payoff to

*x*in a triadic scenario, when*z*is fighting with coalition of*x*and*y**S*3*x*[*CxCy*,*CxCz*,*CyCz*]Payoff to

*x*in a triadic scenario, when there is mutual cooperation/ compromise*i*Discount rate discounting future payoffs to account for time value of payoffs

*X*,*Y*,*Z*Leaders in the world. Also used as

*x*,*y*,*z*when subscripted*Q*(*D*)Level of attack

*D*=*j**Q*(*D*_{zx})Level of attack that denotes the attack is by leader

*Z*on leader*X**Q*(*D*_{z_xy})Level of attack where the attack is by leader

*Z*on the coalition of leader*X*and*Y**Q*(*D*_{ZY_X})Level of attack which denotes that the attack is by the coalition of leaders

*Z*and*Y*on leader*X**Rx*,*Ry*,*Rz*Total resources of

*X*,*Y*,*Z**R*2The total resources in a dyadic interaction

*Rx*+*Ry*=*R*2*R*3The total resources in triadic interaction be

*Rx*+*Ry*+*Rz*=*R*3*Rdy*Disputed or contested Resource share that belongs to Leader

*y*when both*x*and*y*are compromising*Rdx*Disputed or contested Resource share that belongs to Leader

*x*when both*x*and*y*are compromising*Rd*Total pool Disputed or contested Resource that will be shared by the Leaders, when both

*x*and*y*are compromising- Δ
*Kxy*(*Fx*,*Fy*) Changed in dyadic relationships between

*x*and*y*. This is a function of relationships between the leaders as well as the actions taken. This could also be described as Δ*Kxy*(*Dxy*,*Dyx*)- CstB (
*Dxy*) The cost of staging a battle in a dyadic interaction (

*x*launching a battle against*y*)*Px*Probability of winning in a battle, and is proportional to level (effort) of attack (

*Q*(*D*_{ yx })) and relative strength*Ry*/(*Rx*+*Ry*) of the attacker*⇒**Px*=(*Q*(*D*_{ yx })).*Ry*/(*Rx*+*Ry*)*Q*(*D*_{yx})(*Ry*/(*Rx*+*Ry*))*Rdx*The expected loss in a given battle for a target is proportional to the level of attack, likelihood of success and the level of resource contested. This is const.(relative strength of attacker)(contested resource of attacked)

*Q*(*D*_{zx})(*Rz*/*R*3)*Rdx*Expected losses to

*x*due to being attacked by*z*using relative resources available (*Rz*/*R*3). The attack takes place on the contested resource*Rdx*, which belongs to x- emV (
*Fx*,*Cy*) Emotional payoff (non-material utility) for

*X*from*X*fighting while*Y*compromising- emV
_{Tz}(*Fx*,*Cy*) Transitive emotion for

*z*, due to the interaction of*x*,*y*and*z**S**_*.*_**x*(*t*)Refers to the payoff for

*x*in scenario*S**_*.*_*occurring in time step*t*

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