This document provides an overview of game theory. It defines game theory as the study of how people interact and make decisions in strategic situations, using mathematical models. It discusses the history and key concepts of game theory, including players, strategies, payoffs, assumptions of rationality and perfect information. It provides examples of zero-sum and non-zero-sum games like the Prisoner's Dilemma. The document also outlines the key elements of a game and different types of game theory, and discusses applications in economics, computer science, military strategy, biology and other fields.
I provide a (very) brief introduction to game theory. I have developed these notes to
provide quick access to some of the basics of game theory; mainly as an aid for students
in courses in which I assumed familiarity with game theory but did not require it as a
prerequisite
I provide a (very) brief introduction to game theory. I have developed these notes to
provide quick access to some of the basics of game theory; mainly as an aid for students
in courses in which I assumed familiarity with game theory but did not require it as a
prerequisite
3.3 Game TheoryGame theory is a branch of applied mathematics, w.docxgilbertkpeters11344
3.3 Game Theory
Game theory is a branch of applied mathematics, which deals with multi-person decision making situations. The basic assumption is that the decision makers pursue some well-defined objectives and take into account their knowledge or expectations of the other decision makers’ behavior. Many applications of game theory are related to economics, but it has been applied to numerous fields ranging from law enforcement [19] to voting decisions in European Union [20].
There are two main ways to capitalize game theory. It can be used to analyze existing systems or it can be used as a tool when designing new systems. Existing systems can be modeled as games. The models can be used to study the properties of the systems. For example, it is possible to analyze the effect of different kind of users on the system. The other approach is implementation theory, which is used when designing a new system. Instead of fixing a game and analyzing its outcome, the desired outcome is fixed and a game ending in that outcome is looked for. When a suitable game is discovered, a system fulfilling the properties of the game can be implemented.
Most game theoretical ideas can be presented without mathematics; hence we give only some formal definitions. Also, introduce one classical game, the prisoner’s dilemma which we use to demonstrate the concepts of game theory.
3.3.1 Prisoner’s Dilemma
In the prisoner’s dilemma, two criminals are arrested and charged with a crime. The police do not have enough evidence to convict the suspects, unless at least one confesses. The criminals are in separate cells, thus they are not able to communicate during the process. If neither confesses, they will be convicted of a minor crime and sentenced for one month. The police offer both the criminals a deal. If one confesses and the other does not, the confessing one will be released and the other will be sentenced for 9 months. If both confess, both will be sentenced for six months. The possible actions and corresponding sentences of the criminals are given in Table 3.1.
Criminal 2
Don’t confess
Confess
Criminal 1
Don’t confess
-1,-1
-9,0
Confess
0,-9
-6,-6
Table 3.1: Prisoner’s dilemma
3.3.2 Assumptions and Definitions
Game: A game consists of players, the possible actions of the players, and consequences of the actions. The players are decision makers, who choose how they act. The actions of the players result in a consequence or outcome. The players try to ensure the best possible consequence according to their preferences.
The preferences of a player can be expressed either with a utility function, which maps every consequence to a real number, or with preference relations, which define the ranking of the consequences. With mild assumptions, a utility function can be constructed if the preference relations of a player are known [21].
Rationality: The most fundamental assumption in game theory is rationality. Rational players are assumed to maximize their payoff. If t.
This presentation is an attempt to introduce Game Theory in one session. It's suitable for undergraduates. In practice, it's best used as a taster since only a portion of the material can be covered in an hour - topics can be chosen according to the interests of the class.
The main reference source used was 'Games, Theory and Applications' by L.C.Thomas. Further notes available at: http://bit.ly/nW6ULD
how to sell pi coins in South Korea profitably.DOT TECH
Yes. You can sell your pi network coins in South Korea or any other country, by finding a verified pi merchant
What is a verified pi merchant?
Since pi network is not launched yet on any exchange, the only way you can sell pi coins is by selling to a verified pi merchant, and this is because pi network is not launched yet on any exchange and no pre-sale or ico offerings Is done on pi.
Since there is no pre-sale, the only way exchanges can get pi is by buying from miners. So a pi merchant facilitates these transactions by acting as a bridge for both transactions.
How can i find a pi vendor/merchant?
Well for those who haven't traded with a pi merchant or who don't already have one. I will leave the telegram id of my personal pi merchant who i trade pi with.
Tele gram: @Pi_vendor_247
#pi #sell #nigeria #pinetwork #picoins #sellpi #Nigerian #tradepi #pinetworkcoins #sellmypi
how can I sell my pi coins for cash in a pi APPDOT TECH
You can't sell your pi coins in the pi network app. because it is not listed yet on any exchange.
The only way you can sell is by trading your pi coins with an investor (a person looking forward to hold massive amounts of pi coins before mainnet launch) .
You don't need to meet the investor directly all the trades are done with a pi vendor/merchant (a person that buys the pi coins from miners and resell it to investors)
I Will leave The telegram contact of my personal pi vendor, if you are finding a legitimate one.
@Pi_vendor_247
#pi network
#pi coins
#money
3.3 Game TheoryGame theory is a branch of applied mathematics, w.docxgilbertkpeters11344
3.3 Game Theory
Game theory is a branch of applied mathematics, which deals with multi-person decision making situations. The basic assumption is that the decision makers pursue some well-defined objectives and take into account their knowledge or expectations of the other decision makers’ behavior. Many applications of game theory are related to economics, but it has been applied to numerous fields ranging from law enforcement [19] to voting decisions in European Union [20].
There are two main ways to capitalize game theory. It can be used to analyze existing systems or it can be used as a tool when designing new systems. Existing systems can be modeled as games. The models can be used to study the properties of the systems. For example, it is possible to analyze the effect of different kind of users on the system. The other approach is implementation theory, which is used when designing a new system. Instead of fixing a game and analyzing its outcome, the desired outcome is fixed and a game ending in that outcome is looked for. When a suitable game is discovered, a system fulfilling the properties of the game can be implemented.
Most game theoretical ideas can be presented without mathematics; hence we give only some formal definitions. Also, introduce one classical game, the prisoner’s dilemma which we use to demonstrate the concepts of game theory.
3.3.1 Prisoner’s Dilemma
In the prisoner’s dilemma, two criminals are arrested and charged with a crime. The police do not have enough evidence to convict the suspects, unless at least one confesses. The criminals are in separate cells, thus they are not able to communicate during the process. If neither confesses, they will be convicted of a minor crime and sentenced for one month. The police offer both the criminals a deal. If one confesses and the other does not, the confessing one will be released and the other will be sentenced for 9 months. If both confess, both will be sentenced for six months. The possible actions and corresponding sentences of the criminals are given in Table 3.1.
Criminal 2
Don’t confess
Confess
Criminal 1
Don’t confess
-1,-1
-9,0
Confess
0,-9
-6,-6
Table 3.1: Prisoner’s dilemma
3.3.2 Assumptions and Definitions
Game: A game consists of players, the possible actions of the players, and consequences of the actions. The players are decision makers, who choose how they act. The actions of the players result in a consequence or outcome. The players try to ensure the best possible consequence according to their preferences.
The preferences of a player can be expressed either with a utility function, which maps every consequence to a real number, or with preference relations, which define the ranking of the consequences. With mild assumptions, a utility function can be constructed if the preference relations of a player are known [21].
Rationality: The most fundamental assumption in game theory is rationality. Rational players are assumed to maximize their payoff. If t.
This presentation is an attempt to introduce Game Theory in one session. It's suitable for undergraduates. In practice, it's best used as a taster since only a portion of the material can be covered in an hour - topics can be chosen according to the interests of the class.
The main reference source used was 'Games, Theory and Applications' by L.C.Thomas. Further notes available at: http://bit.ly/nW6ULD
how to sell pi coins in South Korea profitably.DOT TECH
Yes. You can sell your pi network coins in South Korea or any other country, by finding a verified pi merchant
What is a verified pi merchant?
Since pi network is not launched yet on any exchange, the only way you can sell pi coins is by selling to a verified pi merchant, and this is because pi network is not launched yet on any exchange and no pre-sale or ico offerings Is done on pi.
Since there is no pre-sale, the only way exchanges can get pi is by buying from miners. So a pi merchant facilitates these transactions by acting as a bridge for both transactions.
How can i find a pi vendor/merchant?
Well for those who haven't traded with a pi merchant or who don't already have one. I will leave the telegram id of my personal pi merchant who i trade pi with.
Tele gram: @Pi_vendor_247
#pi #sell #nigeria #pinetwork #picoins #sellpi #Nigerian #tradepi #pinetworkcoins #sellmypi
how can I sell my pi coins for cash in a pi APPDOT TECH
You can't sell your pi coins in the pi network app. because it is not listed yet on any exchange.
The only way you can sell is by trading your pi coins with an investor (a person looking forward to hold massive amounts of pi coins before mainnet launch) .
You don't need to meet the investor directly all the trades are done with a pi vendor/merchant (a person that buys the pi coins from miners and resell it to investors)
I Will leave The telegram contact of my personal pi vendor, if you are finding a legitimate one.
@Pi_vendor_247
#pi network
#pi coins
#money
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The European Unemployment Puzzle: implications from population agingGRAPE
We study the link between the evolving age structure of the working population and unemployment. We build a large new Keynesian OLG model with a realistic age structure, labor market frictions, sticky prices, and aggregate shocks. Once calibrated to the European economy, we quantify the extent to which demographic changes over the last three decades have contributed to the decline of the unemployment rate. Our findings yield important implications for the future evolution of unemployment given the anticipated further aging of the working population in Europe. We also quantify the implications for optimal monetary policy: lowering inflation volatility becomes less costly in terms of GDP and unemployment volatility, which hints that optimal monetary policy may be more hawkish in an aging society. Finally, our results also propose a partial reversal of the European-US unemployment puzzle due to the fact that the share of young workers is expected to remain robust in the US.
Currently pi network is not tradable on binance or any other exchange because we are still in the enclosed mainnet.
Right now the only way to sell pi coins is by trading with a verified merchant.
What is a pi merchant?
A pi merchant is someone verified by pi network team and allowed to barter pi coins for goods and services.
Since pi network is not doing any pre-sale The only way exchanges like binance/huobi or crypto whales can get pi is by buying from miners. And a merchant stands in between the exchanges and the miners.
I will leave the telegram contact of my personal pi merchant. I and my friends has traded more than 6000pi coins successfully
Tele-gram
@Pi_vendor_247
What website can I sell pi coins securely.DOT TECH
Currently there are no website or exchange that allow buying or selling of pi coins..
But you can still easily sell pi coins, by reselling it to exchanges/crypto whales interested in holding thousands of pi coins before the mainnet launch.
Who is a pi merchant?
A pi merchant is someone who buys pi coins from miners and resell to these crypto whales and holders of pi..
This is because pi network is not doing any pre-sale. The only way exchanges can get pi is by buying from miners and pi merchants stands in between the miners and the exchanges.
How can I sell my pi coins?
Selling pi coins is really easy, but first you need to migrate to mainnet wallet before you can do that. I will leave the telegram contact of my personal pi merchant to trade with.
Tele-gram.
@Pi_vendor_247
how to sell pi coins in all Africa Countries.DOT TECH
Yes. You can sell your pi network for other cryptocurrencies like Bitcoin, usdt , Ethereum and other currencies And this is done easily with the help from a pi merchant.
What is a pi merchant ?
Since pi is not launched yet in any exchange. The only way you can sell right now is through merchants.
A verified Pi merchant is someone who buys pi network coins from miners and resell them to investors looking forward to hold massive quantities of pi coins before mainnet launch in 2026.
I will leave the telegram contact of my personal pi merchant to trade with.
@Pi_vendor_247
Latino Buying Power - May 2024 Presentation for Latino CaucusDanay Escanaverino
Unlock the potential of Latino Buying Power with this in-depth SlideShare presentation. Explore how the Latino consumer market is transforming the American economy, driven by their significant buying power, entrepreneurial contributions, and growing influence across various sectors.
**Key Sections Covered:**
1. **Economic Impact:** Understand the profound economic impact of Latino consumers on the U.S. economy. Discover how their increasing purchasing power is fueling growth in key industries and contributing to national economic prosperity.
2. **Buying Power:** Dive into detailed analyses of Latino buying power, including its growth trends, key drivers, and projections for the future. Learn how this influential group’s spending habits are shaping market dynamics and creating opportunities for businesses.
3. **Entrepreneurial Contributions:** Explore the entrepreneurial spirit within the Latino community. Examine how Latino-owned businesses are thriving and contributing to job creation, innovation, and economic diversification.
4. **Workforce Statistics:** Gain insights into the role of Latino workers in the American labor market. Review statistics on employment rates, occupational distribution, and the economic contributions of Latino professionals across various industries.
5. **Media Consumption:** Understand the media consumption habits of Latino audiences. Discover their preferences for digital platforms, television, radio, and social media. Learn how these consumption patterns are influencing advertising strategies and media content.
6. **Education:** Examine the educational achievements and challenges within the Latino community. Review statistics on enrollment, graduation rates, and fields of study. Understand the implications of education on economic mobility and workforce readiness.
7. **Home Ownership:** Explore trends in Latino home ownership. Understand the factors driving home buying decisions, the challenges faced by Latino homeowners, and the impact of home ownership on community stability and economic growth.
This SlideShare provides valuable insights for marketers, business owners, policymakers, and anyone interested in the economic influence of the Latino community. By understanding the various facets of Latino buying power, you can effectively engage with this dynamic and growing market segment.
Equip yourself with the knowledge to leverage Latino buying power, tap into their entrepreneurial spirit, and connect with their unique cultural and consumer preferences. Drive your business success by embracing the economic potential of Latino consumers.
**Keywords:** Latino buying power, economic impact, entrepreneurial contributions, workforce statistics, media consumption, education, home ownership, Latino market, Hispanic buying power, Latino purchasing power.
The secret way to sell pi coins effortlessly.DOT TECH
Well as we all know pi isn't launched yet. But you can still sell your pi coins effortlessly because some whales in China are interested in holding massive pi coins. And they are willing to pay good money for it. If you are interested in selling I will leave a contact for you. Just telegram this number below. I sold about 3000 pi coins to him and he paid me immediately.
Telegram: @Pi_vendor_247
Poonawalla Fincorp and IndusInd Bank Introduce New Co-Branded Credit Cardnickysharmasucks
The unveiling of the IndusInd Bank Poonawalla Fincorp eLITE RuPay Platinum Credit Card marks a notable milestone in the Indian financial landscape, showcasing a successful partnership between two leading institutions, Poonawalla Fincorp and IndusInd Bank. This co-branded credit card not only offers users a plethora of benefits but also reflects a commitment to innovation and adaptation. With a focus on providing value-driven and customer-centric solutions, this launch represents more than just a new product—it signifies a step towards redefining the banking experience for millions. Promising convenience, rewards, and a touch of luxury in everyday financial transactions, this collaboration aims to cater to the evolving needs of customers and set new standards in the industry.
how to sell pi coins on Bitmart crypto exchangeDOT TECH
Yes. Pi network coins can be exchanged but not on bitmart exchange. Because pi network is still in the enclosed mainnet. The only way pioneers are able to trade pi coins is by reselling the pi coins to pi verified merchants.
A verified merchant is someone who buys pi network coins and resell it to exchanges looking forward to hold till mainnet launch.
I will leave the telegram contact of my personal pi merchant to trade with.
@Pi_vendor_247
Resume
• Real GDP growth slowed down due to problems with access to electricity caused by the destruction of manoeuvrable electricity generation by Russian drones and missiles.
• Exports and imports continued growing due to better logistics through the Ukrainian sea corridor and road. Polish farmers and drivers stopped blocking borders at the end of April.
• In April, both the Tax and Customs Services over-executed the revenue plan. Moreover, the NBU transferred twice the planned profit to the budget.
• The European side approved the Ukraine Plan, which the government adopted to determine indicators for the Ukraine Facility. That approval will allow Ukraine to receive a EUR 1.9 bn loan from the EU in May. At the same time, the EU provided Ukraine with a EUR 1.5 bn loan in April, as the government fulfilled five indicators under the Ukraine Plan.
• The USA has finally approved an aid package for Ukraine, which includes USD 7.8 bn of budget support; however, the conditions and timing of the assistance are still unknown.
• As in March, annual consumer inflation amounted to 3.2% yoy in April.
• At the April monetary policy meeting, the NBU again reduced the key policy rate from 14.5% to 13.5% per annum.
• Over the past four weeks, the hryvnia exchange rate has stabilized in the UAH 39-40 per USD range.
how to sell pi coins at high rate quickly.DOT TECH
Where can I sell my pi coins at a high rate.
Pi is not launched yet on any exchange. But one can easily sell his or her pi coins to investors who want to hold pi till mainnet launch.
This means crypto whales want to hold pi. And you can get a good rate for selling pi to them. I will leave the telegram contact of my personal pi vendor below.
A vendor is someone who buys from a miner and resell it to a holder or crypto whale.
Here is the telegram contact of my vendor:
@Pi_vendor_247
What price will pi network be listed on exchangesDOT TECH
The rate at which pi will be listed is practically unknown. But due to speculations surrounding it the predicted rate is tends to be from 30$ — 50$.
So if you are interested in selling your pi network coins at a high rate tho. Or you can't wait till the mainnet launch in 2026. You can easily trade your pi coins with a merchant.
A merchant is someone who buys pi coins from miners and resell them to Investors looking forward to hold massive quantities till mainnet launch.
I will leave the telegram contact of my personal pi vendor to trade with.
@Pi_vendor_247
Even tho Pi network is not listed on any exchange yet.
Buying/Selling or investing in pi network coins is highly possible through the help of vendors. You can buy from vendors[ buy directly from the pi network miners and resell it]. I will leave the telegram contact of my personal vendor.
@Pi_vendor_247
1. Presentation on
Game theory
Presented to Presented by
Dr. Hulas Pathak Navin Chandra Das
Professor M.Sc.(Ag.) Pre. Year
Deptt. Of Agril. Economics Deptt. Of Agril. Economics
College of Agriculture Raipur (C.G.)
2. Game Theory
Game theory is the study of how people interact
and make decisions.
This broad definition applies to most of the social sciences,
but game theory applies mathematical models to this
interaction under the assumption that each person's behavior
impacts the well-being of all other participants in the game.
These models are often quite simplified abstractions of real-
world interactions.
3. History of Game Theory
Game theoretic notions go back thousands of
years
– Talmud and Sun Tzu's writings.
Modern theory credited to John von Neumann
and Oskar Morgenstern 1944.
– Theory of Games and Economic Behavior. In the early
1950s,
John Nash (“A Beautiful Mind” fame)
generalized these results and provided the basis
of the modern field.
4. Meaning of game theory
Game theory is the study of the strategic
interaction among rational players.
The games studied can be quite serious and are
studied in many areas of the natural and social
sciences: military, political and marketing
campaign strategy can be modeled with game
theory, also phenomena in natural science, for
example, in the study of evolutionary biology.
5. Definition of game:-
The interactive situation, specified by the set of
participants, the possible courses of action of each
agent, and the set of all possible utility payoffs, is
called a game; the agents 'playing' a game are called
the players
In a competitive situation the course of action
(alternatives) for each competitor may be either
finite or infinite .A competitive situation will be
called ‘’Game’’ .
6. Basic terms related to game theory
1. Players
2.Strategy.
a. Pure strategy
b. mixed strategy
3. Optimum strategy
4. Value of game
5.Payoff matrix
7. Game theory: assumptions
(1) Each decision maker has available to
him two or more well-specified choices or
sequences of choices.
(2) Every possible combination of plays
available to the players leads to a well-
defined end-state (win, loss, or draw) that
terminates the game.
(3) A specified payoff for each player is
associated with each end-state.
8. Assumption con…
4.Each decision maker has perfect
knowledge of the game and of his
opposition.
(5) All decision makers are rational; that is,
each player, given two alternatives, will
select the one that yields him the greater
payoff
9. Use Of Game Theory
Economists
innovated antitrust policy
auctions of radio spectrum licenses for cell phone
program that matches medical residents to hospitals.
Computer scientists
new software algorithms and routing protocols
Game AI
Military strategists
nuclear policy and notions of strategic deterrence.
Sports coaching staffs
run versus pass or pitch fast balls versus sliders.
Biologists
what species have the greatest likelihood of extinction.
10. Game Theory
For Game Theory, our focus is on games where:
– There are 2 or more players.
– There is some choice of action where strategy matters.
– The game has one or more outcomes, e.g. someone wins,
someone loses.
– The outcome depends on the strategies chosen by all players;
there is strategic interaction.
What does this rule out?
– Games of pure chance, e.g. lotteries, slot machines. (Strategies
don't matter).
– Games without strategic interaction between players, e.g.
Solitaire.
11. Elements of a Game
1. The players
• how many players are there?
• does nature/chance play a role?
2. A complete description of what the players can do –
the set of all possible actions.
3. The information that players have available when
choosing their actions
4. A description of the payoff consequences for each
player for every possible combination of actions
chosen by all players playing the game.
5. A description of all players’ preferences over
payoffs.
12. 12
Types of Game Theory
1. Two-person constant sum game theory
3. Two-person zero sum game theory (e.g., prisoner’s dilemma)
Saddle point
4. Mixed strategy
5. The rectangular game as linear progamming
13. Zero-Sum vs. Non-zero-Sum
In a zero-sum game, a player’s gain is equal
to another player’s loss.
In a non-zero-sum game, a player’s gain is
not necessarily equal to another player’s
loss.
14. Two-Person Zero-Sum Game
Payoff/penalty table (zero-sum table):
– shows “offensive” strategies (in rows) versus
“defensive” strategies (in columns);
gives the gain of row player (loss of column
player), of each poTwo decision makers’ benefits
are completely opposite
i.e., one person’s gain is another person’s loss
– ssible strategy encounter
15. Example 1 (payoff/penalty table
Athlete Manager’s Strategies
Strategies (Column Strategies)
(row strat.) A B C
1 $50,000 $35,000 $30,000
2 $60,000 $40,000 $20,000
16. Two-Person Constant-Sum Game
For any strategy encounter, the row
player’s payoff and the column player’s
payoff add up to a constant C.
It can be converted to a two-person zero-
sum game by subtracting half of the
constant (i.e. 0.5C) from each payoff
17. Example 2 (2-person, constant-sum
During the 8-9pm time slot, two
broadcasting networks are vying for an
audience of 100 million viewers, who
would watch either of the two networks.
18. Payoffs of NW1 for the constant-sum
of 100(million
Network 1 Network 2 (NW2)
(NW1) western Soap Comedy
western 35 15 60
soap 45 58 50
comedy 38 14 70
19. An equivalent zero-sum table
Network 2
Network 1 western Soap Comedy
western -15 -35 10
soap - 5 8 0
comedy -12 -36 20
20. Equilibrium point
• In a two-person zero-sum
game, if there is a payoff value
P such that
P = max{row minimums}
= min{column maximums}
then P is called the equilibrium point, or
saddle point, of the game
21. The Prisoners' Dilemma Game
Two players, prisoners 1, 2.
Each prisoner has two possible actions.
– Prisoner 1: Don't Confess, Confess
– Prisoner 2: Don't Confess, Confess
Players choose actions simultaneously without
knowing the action chosen by the other.
Payoff consequences quantified in prison years.
– If neither confesses, each gets 1 year
– If both confess, each gets 5 years
– If 1 confesses, he goes free and other gets 15 years
Fewer years=greater satisfaction=>higher payoff.
– Prisoner 1 payoff first, followed by prisoner 2 payoff.
22. Prisoners’ Dilemma in “Normal”
or “Strategic” Form
Don’t
Confess
Confess
Don’t
Confess
1,1 15,0
Confess 0,15 5,5
23. Prisoner’s Dilema
Prisoners’ Dilemma in “Normal” or “Strategic” Form
Prisoners’ Dilemma in “Normal” or “Strategic” Form
Prisoners’ Dilemma in “Normal” or “Strategic” Form
Prisoners’ Dilemma in “Normal” or “Strategic” Form
Prisoners’ Dilemma in “Normal” or “Strategic” Form
Prisoners’ Dilemma in “Normal” or “Strategic” Form
Prisoners’ Dilemma in “Normal” or “Strategic” Form
Prisoners’ Dilemma in “Normal” or “Strategic” Form
Prisoners’ Dilemma in “Normal” or “Strategic
24. Prisoners' Dilemma :
Example of Non-Zero Sum Game
A zero-sum game is one in which the players'
interests are in direct conflict, e.g. in football, one
team wins and the other loses; payoffs sum to
zero.
A game is non-zero-sum, if players interests are
not always in direct conflict, so that there are
opportunities for both to gain.
For example, when both players choose Don't
Confess in the Prisoners' Dilemma
25. Prisoners' Dilemma :
Application to other areas
Nuclear arms races.
Dispute Resolution and the decision to hire
a lawyer.
Corruption/political contributions between
contractors and politicians.
Can you think of other applications?