<style> .reveal section img { background: none; border: none; } </style> # [Game Theory](https://en.wikipedia.org/wiki/Game_theory) Doug, 2020-02-10 --- ## Aim to cover - What it is - Why I think it's cool - How to use it --- ## Personal interest <p class="fragment" data-fragment-index="1"> Sometimes people cooperate... </p> <p class="fragment" data-fragment-index="2"> Sometimes people compete... </p> <p class="fragment" data-fragment-index="3"> Sometimes people fight... </p> <p class="fragment" data-fragment-index="4"> ... the <i>same</i> people </p> <img src="http://discordemoji.com/assets/emoji/ThinkItaly.png" style="width:200px" class="fragment" data-fragment-index="5"> --- ### Assumptions - people have _some_ degree of choice - i.e. not inescapably locked into their patterns <br> <br> ### Questions - How can people be shifted to better patterns? - How can people _shift themselves_ to better patterns? --- ## Wikipedia wisdom > Game theory is the study of mathematical models of strategic interaction among ~~rational~~ decision-makers. (Scorethrough added) --- ## Consider Risk  --- ## Risk components <p class="fragment" data-fragment-index="1"> <b>players</b>: up to 5 </p> <p class="fragment" data-fragment-index="2"> <b>objectives</b>: to win (world domination/mission cards) </p> <p class="fragment" data-fragment-index="3"> <b>rules</b>: define allowable moves </p> <p class="fragment" data-fragment-index="4"> <b>strategies</b>: effective sequences to achieve obj. </p> <p class="fragment" data-fragment-index="5"> <b>outcomes</b>: someone wins/everyone gives up </p> --- ## Another game? --- ## Players - how many? - will they 'play' again? - do they care about the others opinion? <p class="fragment" data-fragment-index="1"> <b>G.T. →</b>: players abstracted to Player A and B, or Player and Group. Individual differences limited to... </p> --- ## Objectives - do players have the same or different objective? - are the objectives intrinsically competitive or not? - cake slicing vs cake baking <p class="fragment" data-fragment-index="1"> <b>G.T. →</b>: abstracted to comparative units, <a href="https://en.wikipedia.org/wiki/Cardinal_utility">'utils'</a> (e.g. apple (+3), pear (+10), moldy grape (-2)) </p> --- ## Rules - some 'rules' are environmental constraints - can players communicate? - some rules are social - can therefore be broken: cheating possible! - enforcement must be accounted for <p class="fragment" data-fragment-index="1"> <b>G.T. →</b>: rules summarized in 'game scenario' which accounts for environmental constraints and social rules </p> --- ## Strategies - random gameplay usually suboptimal - strategy for one player may be affected by strategy of another - strategy may equilibriate in certain circumstances <p class="fragment" data-fragment-index="1"> <b>G.T. →</b>: strategies largely result from player objectives + rules. May be predicted, simulated and tested </p> --- ## Outcomes - Current state and/or result - Not necessarily what the players want(ed)! <p class="fragment" data-fragment-index="1"> <b>G.T. →</b>: measured as a util-sum for each player </p> --- ## 'Real' games When you start playing poker with money...  (i.e. the outcome affects you *after* playing) --- ## [Prisoners Dilemma](https://en.wikipedia.org/wiki/Prisoner%27s_dilemma)  --- ## P.D. generic  --- ## What's your best strategy? ---  --- ## What's your best strategy? For you—and you alone—the only good strategy is to 'defect' :persevere: Cooperation only makes sense if you _really_ trust and care about the other. Used by economists to falsely justify privatization :angry: --- ## [Stag Hunt](https://en.wikipedia.org/wiki/Stag_hunt)  --- ## Multiplayer games Goodbye grids, hello trees  <br> $$ Outcomes = Options^{Players} $$ --- ## Oh the games we could play! [List of Game Theory Games](https://en.wikipedia.org/wiki/List_of_games_in_game_theory) --- ## Application - to rationalize British/German non-agression in WW1 - to account for triumph/tragedy of the commons <p class="fragment" data-fragment-index="1"> <b>Generally solving collective issues</b> </p> --- ## In communities Gerry does some annoying stuff. Everyone in the community would benefit if someone stopped him. The 'someone' would take a relatively big risk of Gerry not liking them.  --- ## ['Volunteer's dilemma'](https://en.wikipedia.org/wiki/Volunteer%27s_dilemma)  ---  <p class="fragment" data-fragment-index="1"> What have we done at Kanthaus to make sanctioning/volunteering easier? </p> --- ## In communities 2 You're scheduling with Luna. You'd prefer to meet at 5, she'd prefer to meet at 6, but you'd both prefer either time than to continue talking about it.  --- ## ['Bach or Stravinsky'](https://en.wikipedia.org/wiki/Battle_of_the_sexes_(game_theory))  --- ## Bigger scenarios - All fishermen would benefit if less fish were caught - but each fisherman has the incentive to catch more - Data-privacy concerned people would benefit if everyone used **x** - but people already using other protocols --- ## Summary: properties - Human incentive interested - Amoral - Outcome oriented - Generalized/simplified model of real-world - Comparable scenarios (common description language) --- ## Summary: opportunities <p class="fragment" data-fragment-index="1"> <b>outcomes</b>: <b>what you want to change</b>, but determined by... </p> <p class="fragment" data-fragment-index="2"> <b>strategies</b>: determined by... </p> <p class="fragment" data-fragment-index="3"> <b>rules</b>: ← <b>intervention opportunities</b> </p> <p class="fragment" data-fragment-index="3"> <b>objectives</b> ← <b>intervention opportunities</b> </p> <p class="fragment" data-fragment-index="4"> <b>players</b>: limited opportunities </p> ---