Article (Hurwitz2007) Hurwitz, E. & Marwala, T. Multi-Agent Modeling Using Intelligent Agents in the Game of Lerpa CoRR, 2007, abs/0706.0280
the traditional game-theory approach (mathematical, and statistical) is not good enough to many complex games where the number of players are more than 3
Multi agent modelling approach models the behavior of agents rather than the whole system and uses a bottom-up approach to predict the nature of the system.
Game-Theory explained … ( assumptions when finding these dominant strategies,
2.1 Limitations of Game-Theory
The “trembling hand” problem , players are not always rational
Game theory cannot handle more than two to three players and is applied to relatively simple games
By utilizing multi-agent modeling, it is possible to solve a number of problems that are unsolvable using traditional game-theory
3 Multi-Agent Modelling involves breaking a system up into its component features, and modeling those components 
3.1 Emergent Behavior: the simple interactions between agents produce complex results 
John Conway’s game of artificial life provides an excellent illustration
of emergent behavior, and the ramifications thereof .
… see, the rules are incredibly simple, but the consequences of these rules … (i.e. glider)
3.2 Advantages of Multi-Agent Modeling
Agents are far simpler to model than the overall system
The emergent behavior resulting from the agent interactions implies that systems too complex to be traditionally modeled can now be tackled, since the complexity of the system need not be explicitly modeled.
Large systems with heterogeneous agents can be easily handled within a MAS
… it is difficult to state with any degree of certainty as to why a certain outcome has been arrived at .
validation of the model becomes an important aspect of any MAS.
3.4 MAM Applications
3.4.1 Swarm Theory  utilize many simple agents to work together to achieve a larger, common goal (Swarm of ants)
… systems depend on the engineer’s ability to predict the (often unexpected) emergent behavior of the system for given agent behavior.
3.4.2 Complexity Modelling : modeling complex systems that are often too complex to be explicitly modeled using the traditional, and often insufficient, mathematical models 
Applied Computational Economics (ACE), applies a bottom-up approach to modeling an economic system, rather than top-down approach , which requires full system specification and then component decomposition .
3.4.4 Social Sciences
3.5 Making a Multi-agent Model
4 Intelligent Agents
reinforcement learning .
4.1 What is Intelligence?
able to :
learn from its own inferences, without being taught
drawing conclusions from incomplete data, based on its own knowledge
re-evaluate its own knowledge, and adapt if necessary
Reinforcement learning involves the training of an artificial intelligence system by trial-and-
error is very well suited to episodic tasks , appropriate in the field of game-playing, where many episodes are encountered before a final result is reached
4.2.1 Rewards and Returns  goal or target to strive towards 
… make a decision that has a lower initial reward than other options, but maximizing its future return.. likened to making a sacrifice in chess …
4.2.2 Exploitation vs Exploration 
utilization of gained knowledge to maximize returns is termed Exploitation
5 Neural Networks
… to be read
6 Tic Tac Toe
… to be read
is a card game, While not a well-known game, it is an ideal testbed application for intelligent agent.
8 Lerpa MAM
three decision-making stages
• Whether to play the hand, or drop (knock or fold)
• Which card to play first
• Which card to play second
8.2 Agent AI Design
type of learning to be implemented needs to be chosen, … neural network architecture. … the design of the inputs to the neural network, as these determine what the agent can ‘see’ at any given point … determine what assumptions
9 The Intelligent Model
9.1 Agent Learning Verification
agent decides that the risks are too great, and does not play any more …
agent must be given enough ‘courage’ to play to learn .. so it was forced to play the first 200 hands and then left to its own devices
9.3 MAS Learning Patterns
9.4 Agent Adaptation
9.5 Strategy analysis
… intelligent agents do in fact learn to bluff
9.8 Personality Profiling
A good player should not be limited to assuming rationality from his opponents, but rather should identify his opponents’ characteristics and exploit their weaknesses. To do this, one needs to create “personality” types in agents, (e.g. aggressive or conservative personality)