| [[19-01-01-Cognition | cognition]], [[13-01-01-Motivation | motivation]] |
John Von Neumann -create game theory. Theory of game and economic behaviour
W co grają ludzie - Berne Eric Influence book
- what u do
- when u do
Game Types
Mathematical modeling at strategic interaction between rational agents.
- action of one player influence other players (concept of strategic interdependence)
- assumption that agents act rationally. (rational bah not always conform to reality)
Players, strategy, payoff.
process:
- Make assumptions - thought process came from Assumptions. Can dispute, criticize ect… (Carefully with assumptions)
- Do math - can not dispute
- Reach conclusion
Game theory to work need rational actors
Human Behavioral Biology
Personality
Game Mechanics
- In lot of species there is no cognitive strategy
- In real live multiple goals and multiple games
Number of Players
- Two
- More players
Progression
- Turn based
- Simultaneous move
Number of Rounds
- Infinite
- Repeated
Repeated play increase cooperation
Information availability
- Perfect - known information
- Incomplite -> Bayesian Nash equilibrium, perfect Bayesian equilibrium
- Depth limited search.
Zero Sum Game
- Interest is not overlapping.
win-lose
Approaches to Conflict
Cooperative
How to be fair - Group best effort, coalition and benefit and contribution type in coalition
Shapley Value
- method of dividing gains or costs among players according to value of individual contribution
Marginal Contribution
- Determined by what is gain or lost by removing them from the game
- Dummy player have 0 value
If 2 parties bring same things to coalition, they should have to contribute the same amount & should be rewarded for their contributions equal.
Pareto efficiency
Outcome is Pareto optimal if there is no outcome that makes at least one player better off without making any player worse off.
Competitive
How to be smart - Actor best interest - sub optimal solution in the long run
Nash equilibrium
optimal outcome of a game is where no player have incentives to deviate from initial strategy.
(decide to be better off no matter what opponent will do) (rational play when more then one player. not only define start but always believes) Every player play best response strategy to what other doing. Knowing other strategies and have no incentives to cheat. Everyone want to keep it without policing
Most games have odd number of equilibria
no player have profitable deviations
Terms
Risk Aversion
how much u willing to pay for insurance
Tragedy of the Commons
Some public good lot of persons contribute no one want to pay cause take a small parts of contribution only.( there is mat trough to compensate )
there are certain optimal strategies and no other GT solution
Commitment problems
You must commit but not sure what B will chose
Ultimatum Game Assumptions - single ultimatum, Take or leave it
Probability distributuin
- advancced strategies games, more revarding
Strategies
qualities that will help to win when need to cooperate:
- Nice
- Forgiving
- Retaliatory (if oponent defect strike back immidietly) (can retaliate 9 of 10 times to reduce error)
- Clear « with complicated program you cannot figure out their strategy. Tit for tat tend to be best. « without signal error in simulation. (when all players rational). most of life is not zero sum.
- exploitive strategies in poker
stoping problem
37% optimal . after 27% of checked options commit to first that is better then
wazne ile rund. im mniej rund tym mniej kooperacji potrzebujesz!!!!!!
Dominant strategy
- best payoff no matter other players moves. ITS EXTENTION IS NASH EQQUILIBRIUM (and more)
MinMax
- minmimize maximum lose. ensure you guarded by worst scenario. (use in zero sum)
Mix Strategy
- play only if there are indifferences in few strategies
Backward Induction
Base on assumption that all future play will be rational. Whenever I’m making move now I should focus on what opponent will do after that. maximizing
Forward Induction
Based on assumption that all past play was rational
Tic Tac Toe
Pavlov strategy
- switch if not working (you can exploit)
TfT
Tit for tatdrove other strategies to extinction and formalize optimal strategy may lose battles but win wars. (Vulnerable of signal error). Start nice cooperating > forgiving > cooperate when you can
FTfT
forgiving tit for tatwitch is more vulnerable for exploitation TfT -> jezeli zaufanie to switch to forgiven TFTF Trust
Madness
- possibility of changes
Strategies to survive forgiving tic for tat (vulnerable to exploit) > forgiven tic for tat after while - counterintuitive moves could help with strength opponents.
Game Theory Optimal
- assumes opponent is always countering with the perfect strategy
- can have lower yield EV then exploitative play
pkr > fint highest EV lines routes possible for have best formulatetd strategy. + balance it to dont be exploited.
but can be not profitable as exploit.
balance stratedy
Exploitative
-humans make a lot errors exploit mistakes exploitative strategy is valuable in the short run after new entry,
Explorative
while explorative strategy is significant in the long run only after new entry.
Jeopardy! Strategy
transitivity-in-game-theory
Games
Poisoner Dilemma
If one round
- always defect to GTO ( Dominant strategy ) - Best outcome regardless what other player does.
| A (COOP) | A (CONFES) | |
|---|---|---|
| B (COOP) | 0 / 0 | 0 / -2 |
| B (CONFES) | -2 / 0 | -1 / -1 |
Stag Hunt
if no lies / neither player deviate
- Stag/Stag (pareto efficient)
- Rabit/Rabit (pareto inefficient) are equilibria’s.
| Stag | Rabbit | |
|---|---|---|
| Stag | 3, 3 | 0 , 2 |
| Rabbit | 2, 0 | 1, 1 |
Coin filps / Matching Pennies
Zero sum game. No pure strategy Nash equilibrium. - If no pure nash exist in mix strategies.
| Heads | Tails | |
|---|---|---|
| Heads | 1, -1 | -1 , 1 |
| Tails | -1, 1 | 1, -1 |
Batle of sexes
| Heads | Tails | |
|---|---|---|
| Heads | 1, 2 | 0 , 0 |
| Tails | 0, 0 | 2, 1 |
A>B>C
| Heads | Tails | |
|---|---|---|
| Heads | B, a | C, c |
| Tails | C, c | A, b |
(1,2) - are nash
combinatorial games
diferential games
TCG - traiding card games
Poker
a game of decision-making in the face of incomplete information.
Basics
Betting rounds & Positions
Out Of Position should only defend hands better than In Position
| Button / Dealer | strongest - 50% opening range / button river betting range (only 57 combos) | In position (Act last) |
|---|---|---|
| Cutoff | second-best position in a hand of poker. | Late Positions |
| HiJack | ||
| LoJack | Tide pairs and Figure + high | |
| Under The Gun +1 | Mid positions | |
| Under The Gun | only ases | (left to the BB Act first Before the flop) |
| BB | defending range calling range 40% (no AA KK QQ - because it wuld be rerange ) play garbage hands priced in (range advantage) | Early position |
| SB | tight is right // in short stack when AllIn - is good (game of chicken ) | Out of position Act first (After flop) |
| High | 1 |
| Pair | 2 |
| 2 Pairs | 2 + 2 |
| Three | 3 |
| Straight | 1..5 |
| Flush (color) | |
| Full House | 2 + 3 |
| Four | 4 |
| Straight | |
| Royal Flush | 1..5 |
Moves
Bet - change
Check - stay in game, no change
Fold -
Call - answer to bet
Check-raise - The player who checked (in anticipation of others raise) then raises in the same round
Limp - Playing minimum bet when u last to act.
Chips
Chips to start: 20-40 BB for shallow tables to 250+ for deep game
EV
EV = chance * $win - (1-chance) * $lose
Other rules
- Ante - Ante and Blinds are forced bets
- Bounty -
pattern visible on table
pair - invisible straight - flush - visible
Strategies
kombninatoryka wazna
- relation of hands u have to opponent hand
- your percived range. Whaty they expected u to have
Combinatorics
ranges / minimum defence frequency (MDF) / correct frequencies for calling, folding, and raising (depending on bet size) / likelihood of your opponent holding specific hands
169 different poker hands:
Hand Range Charts
GTO
Game theory optimal - is not enough agressive. Optimize decisions and build strategies to put opponents in place where they have hard time with optimization their decisions (look for weaknes).
Tells
- How much
Engagementin cards - protect valuable things, close to you vs prefold (away)
- eyes,
- quick glance on chip, thinking about value legs subconcious tels concious tell> playing .. overacting > opposit what trying to convey
- feet forrward >
confidencestrengths - stop chewing gum if scary , exiced chue
- disconnect
- bad cards from the game .
- good cards just no focs on cards , watch for chit chat
https://www.youtube.com/c/Gametheory101/videos
https://www.youtube.com/c/PrimerLearning/videos
Edge:
kelly cryteria
-
max rate of growth should bet small on each
- stay in the game long enough to let law of probabilyty work
- invest more when have more edge
- under/overbet is bad. - excexs leverage will wipe you out
- 20% of stack
–
Bargaining
Bargening dynamics get really complicated really quickly.
| Proposal power | make offers to the other side (accept/reject position not good) |
| Patience | no needing a deal (Tragedy of bargening) ‘rich get richer’ |
| Outside options | |
| Monopoly | Unique quality |
| Knowledge | knowledge of the others sides minimum value dont know choose between lesser of two evils |
| Reputation | |
| Credible commitment | contracts good / black market bad |
| Costly signals of higher value |
War
(international relations)
- war inefficiency puzzle
- preventive war
- preemptive war
jak zapobiegać wojnie.
- kraje handlujące ze sobą mniej wojen (world with trade consume more )
- koszty
Bio
r/K selection theory trade off between quantity and quality of offspring. r (left), K (right) strategies.
- coordination problem
- mysia utopia
SOMETIMES: burning money help to increes payof !!!!!!!!!
Tactics
- odciecie od zaopatrzenia
- wysokość - pozycja
-
nacierajacy x3 sil (latwiej bronic)
-
pogoda gdzie sie przemieszczać
# standaard deviation
https://www.google.com/search?q=standard+deviation&source=lmns&bih=786&biw=1597&hl=en&sa=X&ved=2ahUKEwiatuLygbb6AhWJAhAIHfmlCZ4Q_AUoAHoECAEQAA