Effect of Information on Collusion Strategies in Single winner, multi-agent games
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Transcript of Effect of Information on Collusion Strategies in Single winner, multi-agent games
Effect of Information on Collusion Strategies in
Single winner, multi-agent games
December 2, 2010
Nick GramskyKen Knudsen
Contents
1. Motivation
2. Identification of Collusion
3. Classification of Coalitions
4. Implementation
5. Results
6. Conclusions
Motivation
Explicit Collusions Alliances Survival Truces
Implicit Collusions Minimax against strongest
player Tit-for-tat
Reasons to Collude Improve position relative to other agent(s) Self-preservation / Survival
Contents
1. Motivation
2. Identification of Collusion
3. Classification of Coalitions
4. Implementation 5. Results
6. Conclusions
Identification
Find course grained collusive behavior
1. Offensive-based collusion Multiple agents attacking a single agent for a fixed
number of rounds In our examples, we limited this to 1 round.
2. Defensive-based collusion Multiple agents not attacking each other over a fixed
number of rounds. In our examples, we limited this to 2 rounds.
IdentificationOffensive based coalitions
IdentificationDefensive based coalitions
Contents
1. Motivation
2. Identification of Collusion
3. Classification of Coalitions
4. Implementation
5. Results
6. Conclusions
1. Socially inclined behavior For some predefined time, if target satisfies the
following, then we define the actions of the attacking players as being 'socially oriented‘
h(x) is a heuristic function for any adversary. vh(x) when dealing with different layers of fog
2. Else: Some other collusive behavior
Classification Offensive based behaviors
Classification Offensive based algorithm
Classification Defensive based algorithm
ClassificationMissed opportunities
Classify a missed opportunity by finding players that: for a predefined period were not attacked
above a certain percentage and… satisfy either their power heuristic or visual
heuristic (below) threshold
Contents
1. Motivation
2. Identification of Collusion
3. Classification of Coalitions
4. Implementation
5. Results
6. Conclusions
Implementation
Used Warfish to play games of Risk. Free website warfish.net
Risk is a zero-sum game where players seek (simulated) world
domination!
Only one winner, the last remaining contestant.
Attacks are made via dice (random number generator)
Amass armies, grow in power, rule the world! Or at least the world represented on a board...
ImplementationEnvironment
Reduced resource strategies
Randomized players
Set card trade-in values to be constant (5)
Disabled card capture on elimination
Multiple map types Larger than original Risk board Reduces board specific strategies in analysis
ImplementationWorld Map
ImplementationEurope Map
ImplementationFog of War
Varied amount of information available to all agents via different levels of 'fog of war'.
6 different levels of fog available in game Level 0: No fog (perfect information) Level 1: See all occupations, neighboring units only Level 2: See all occupations (no units) Level 3: Only see neighboring occupations and units Level 4: See only neighboring occupations Level 5: Complete fog (only know about self)
Tested with 3 levels of fog {0,1,3}
ImplementationOracles
Participants who annotated their strategies and behaviors as games were played
Compared oracle annotations to game data Spot-check that analysis found collusion Though noisy, analysis and annotations were
inline with game history.
Contents
1. Motivation
2. Identification of Collusion
3. Classification of Coalitions
4. Implementation
5. Results
6. Conclusions
ResultsCollusion vs Game length
x-axis: Number of turnsy-axis: Number of "interesting" windowsθh = 1.3 per 1 turn window
ResultsOffensive
1. Players all gang up on Yellow.
2. Validated by Oracle annotations.
Game: 98478150 Map: World Fog Level: 1
ResultsOffensive
1. Minmax against Blue
2. Confirmed by reading through the transcript.1. Blue quickly gained
power
2. Challenged remaining players to team up against him Game: 97976903
Map: Europe Fog Level: 0
“Right now (Yellow) knows that if he does not get both you (Red) and (Green) on his side, this game will be won by me”
ResultsOffensive
x-axis: Number of turnsy-axis: Number of "interesting" windowsθh = 1.3 / 1 turn window
Games 98478150 (left) and 97976903 (right)
ResultsOffensive & Defensive
1. Minimax against strongest player
2. Towards the end of the game, explicit truce between top 2 players
Game: 12069561 Map: Europe Fog Level: 0
Scatter plot of number of windows classified as defensive-oriented for all games.x-axis: number of turns y-axis: number of interesting windowsθ = 0.05
*Game: 12069561
ResultsDefensive
ResultsOracle
1. Oracle self-interest annotations (Blue)
Game: 88318444 Map: World Fog Level: 1
x-axis: Number of turnsy-axis: Number of "interesting" windowsθh = 1.3 / 1 turn window
ResultsFog Level 3
1. Typical of the layer 3 games.
2. Everything breaks down. Players can’t figure out who is in the lead until it is too late.
Game: 67785982 Map: Europe Fog Level: 3
Results
Collusion % is percentage of available windows where remaining players direct more than 75% of attacks towards target.
Social % is percentage of available windows with same criteria as above BUT the target satisfies heuristic thresholds from earlier
θh = 1.3 / 1 turn window
Target’s residual power 43.3% (4-player) 65% (3 player)
θh = 1.6 / 1 turn window
Target’s residual power 53.3% (4-player) 80% (3 player)
ResultsEurope Map
θh = 1.3 θh = 1.6
ResultsWorld Map
θh = 1.3 θh = 1.6
Contents
1. Motivation
2. Identification of Collusion
3. Classification of Coalitions
4. Implementation
5. Results
6. Conclusions
Conclusions
Presented a basic algorithm to identify and classify collusion
Games with unusually large number of collusive behaviors tended to prolong games beyond the average.
As fog increased (information decreased), collusive behaviors diminished.
Results were consistent across maps.
Level 0 data was consistent between our volunteers and the public.
Analysis supported by Oracle annotations and in-game conversations.
Conclusions
Visual heuristic does not hold well for fog games Based on a knowledge of territories and bonuses
Limited data sets Time limitation
Short time-frame for project Games averaged 20 days to complete
Require more experiments with fog levels
Data integrity Games had large variance in player abilities Players were involved in multiple simultaneous games
May have forgotten strategy Players may have a predefined disposition towards other
players (Social Value Orientation)
ConclusionsFuture Work
Investigate possible equilibrium in collusions versus game length.
Lag response for social orientation.
Once the strongest player is removed from power, it can take a few rounds for the coalition to change strategies.
As information decreases, agents tend to collude less. Why? fairness poor assessment of board
Mix socially oriented bots with human players