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65-410: Massive Assault is a turn-based , computer wargame by Wargaming . Despite featuring 3D graphics, the game is similar to tabletop wargames in that its gameplay is governed by simple rules and takes place on a hexagonal grid. The game's opposing forces are made up of largely equivalent units. Gameplay is made somewhat more complex by the addition of "secret allies," the disclosure of which can change

130-460: A timeline as part of a game mechanic that lets players establish or alter the order of events within the game world. For example, in the indie role-playing game Microscope , players invent a timeline together, then select different segments of the timeline to embellish through roleplaying. In the card game Chrononauts , everyone plays timeline cards to change the order of historical events, creating an alternate history . A progress clock

195-470: A turn-based strategic layer with real-time tactical combat or vice versa. The video games X-COM: Apocalypse (1997), Fallout Tactics (2001) Arcanum: Of Steamworks and Magick Obscura (2001), Pillars of Eternity II: Deadfire (2018), Pathfinder: Kingmaker (2018, added later per patch) and Pathfinder: Wrath of the Righteous (2021) offer the option of turn-based or real-time mode via

260-483: A clear dominant strategy of betrayal where the only strong Nash Equilibrium is for both prisoners to confess. This is because we assume both prisoners to be rational and possessing no loyalty towards one another. Therefore, betrayal provides a greater reward for a majority of the potential outcomes. If B cooperates, A should choose betrayal, as serving 3 months is better than serving 1 year. Moreover, if B chooses betrayal, then A should also choose betrayal as serving 2 years

325-424: A column at the exact same time. Traditionally, within a cell, the first entry is the payoff of the row player, the second entry is the payoff of the column player. The “cell” that is chosen is the outcome of the game. To determine which "cell" is chosen, the payoffs for both the row player and the column player must be compared respectively. Each player is best off where their payoff is higher. Rock–paper–scissors ,

390-496: A configuration setting. In real-time games with an active pause system (also called "pausable real-time" or "real-time with pause"), players can pause the game and issue orders. When the game is un-paused, the orders automatically execute. This offers additional tactical options, such as letting players issue orders to multiple units at the same time. The Baldur's Gate series popularized pausable real-time for mouse-driven party-based computer role-playing games , although

455-447: A deal where they can choose to cooperate with one another by remaining silent, or they can choose betrayal, meaning they testify against their partner and receive a reduced sentence. It should be mentioned that the prisoners cannot communicate with one another. Therefore, resulting in the following payoff matrix: (C ooperation ) (Betrayal) (C ooperation ) Prisoner B: 3 Months (Betrayal) Prisoner B: 3 Years This game results in

520-414: A finite number of options available to choose. An example of a simultaneous 2-player game: A town has two companies, A and B, who currently make $ 8,000,000 each and need to determine whether they should advertise. The table below shows the payoff patterns; the rows are options of A and the columns are options of B. The entries are payoffs for A and B, respectively, separated by a comma. A zero-sum game

585-575: A game action. Turns may represent periods of time, such as hours, days, or years. This is common in 4X video games like the Civilization series and world-building tabletop role-playing games. For example, in Dialect , sets of turns represent eras in a society's development; similarly, in The Quiet Year , each turn represents one week leading up to a community's destruction. This

650-413: A game, it is a complete plan for a player in a given game. Mixed strategies are those in which players randomize strategies in their best responses set. These have associated probabilities with each set of strategies. For simultaneous games, players will typically select mixed strategies while very occasionally choosing pure strategies. The reason for this is that in a game where players don’t know what

715-480: A limited notion of turns in specific instances, such as the free kick in soccer and the free throw and shot clock in basketball. In the card games Nerts and Ligretto , players must compete to discard their cards as quickly as possible and do not take turns. In turn-based games, game flow is partitioned into defined parts, called turns , moves, or plays. Each player is allowed a period of analysis (sometimes bounded, sometimes unbounded) before committing to

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780-404: A pair of stop clocks may be used in order to place an upper limit on turn length. In exchange chess , four players on two teams play on two boards with each team taking one white and one black side. A taken piece can be given to a teammate and placed on their board. A player can abuse this game mechanic by taking an opponent's piece, giving it to a teammate, then waiting unusually long to play

845-551: A player may take during an interrupt sequence is limited by the number of points remaining in the player's action point pool carried over from the previous turn. Examples include the X-COM series of video games, the board wargame Advanced Squad Leader (1985), and attacks of opportunity in Dungeons & Dragons . Newer editions of Dungeons & Dragons also allow a Ready -action to prepare an action to be executed during

910-470: A sequence of turns that is highly variable and has no set order. It is also possible for different players' actions to occur at the same time with respect to the game clock, as in real-time or simultaneously executed games. Examples of video games that use a clock-based system include Typhoon of Steel (1988) and MechForce (1991), both originally for the Amiga . In some games, the sequence of turns depends on

975-417: A simultaneous turn-based game. There are three types of player-alternated games: ranked, round-robin start, and random. The difference is the order in which players start a turn. In ranked player-alternated games, the first player is the same every time. In round-robin games, the first player selection policy is round-robin. Random player-alternated games randomly select the first player. Some games also decide

1040-485: A special card interrupts an opponent's turn to perform an action. In the Mario & Luigi series, the player often has the opportunity to "counterattack" on the enemy's turn, causing damage and often halting the attack. In some turn-based games, not all turns are alike. The board game Imperium Romanum II (1985), for instance, features a "Taxation and Mobilization" phase in every third turn (month), which does not occur in

1105-528: A turn on their own board—thereby allowing the teammate to use the advantage for many future moves on their board. To avoid this, players are often limited to ten seconds per move—with their opponent being allowed to remove one of the player's pawns from the board for each additional ten seconds consumed. The turn-based strategy game Utopia (1982) featured an early example of timed turns. The early Ultima role-playing video games were strictly turn-based, but starting with Ultima III: Exodus (1983), if

1170-484: A widely played hand game, is an example of a simultaneous game. Both players make a decision without knowledge of the opponent's decision, and reveal their hands at the same time. There are two players in this game and each of them has three different strategies to make their decision; the combination of strategy profiles (a complete set of each player's possible strategies) forms a 3×3 table. We will display Player 1's strategies as rows and Player 2's strategies as columns. In

1235-400: Is a payoff of 10 for A which has to be paid by B, therefore a payoff of -10 for B. An example of a simultaneous 3-player game: A classroom vote is held as to whether or not they should have an increased amount of free time. Player A selects the matrix, player B selects the row, and player C selects the column. The payoffs are: All of the above examples have been symmetric. All players have

1300-439: Is a simultaneous game in which there are two players. The decision to be made is whether or not each player wishes to hunt a Stag or a Hare. Naturally hunting a Stag will provide greater utility in comparison to hunting a Hare. However, in order to hunt a Stag both players need to work together. On the other hand, each player is perfectly capable of hunting a hare alone. The resulting dilemma is that neither player can be sure of what

1365-404: Is a tabletop role-playing gamemaster (GM) tool for keeping track of ongoing events that cannot be handled within a single turn, such as the player characters' continuous headway toward defeating a challenge, the gradual approach of an enemy, or a time-limited window of opportunity. The GM draws a segmented circle to represent a clock face, then fills in a segment whenever progress develops toward

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1430-522: Is also common in both video games and tabletop games with dating sim elements. For example, in Persona 5 and Monster Prom , turns represent high school class periods, and in Visigoths vs. Mall Goths , each team's turn represents a specific hour at the mall. Turn-based games come in two main forms: simultaneous or sequential (also called player-alternated ). Diplomacy is an example of

1495-484: Is better than serving 3. The choice to cooperate clearly provides a better outcome for the two prisoners however from a perspective of self interest this option would be deemed irrational. The aforementioned both cooperating option features the least total time spent in prison, serving 2 years total. This total is significantly less than the Nash Equilibrium total, where both cooperate, of 4 years. However, given

1560-470: Is closely linked to Pareto Optimality which is an ideal of Welfare Economics and often implies a notion of ethical consideration. A simultaneous game, for example, is said to reach Pareto optimality if there is no alternative outcome that can make at least one player better off while leaving all other players at least as well off. Therefore, these outcomes are referred to as socially desirable outcomes. The Stag Hunt by philosopher Jean-Jacques Rousseau

1625-548: Is done using real-time and/or turn-based timekeeping. In real-time games, time within the game passes continuously. However, in turn-based games, player turns represent a fixed duration within the game, regardless of how much time passes in the real world. Some games use combinations of real-time and turn-based timekeeping systems. Players debate the merits and flaws of these systems. There are also additional timekeeping methods, such as timelines and progress clocks. In real-time games , time progresses continuously. This may occur at

1690-415: Is important to note that Nash equilibria and many of the aforementioned strategies generally fail to result in socially desirable outcomes. Pareto efficiency is a notion rooted in the theoretical construct of perfect competition . Originating with Italian economist Vilfredo Pareto the concept refers to a state in which an economy has maximized efficiency in terms of resource allocation. Pareto Efficiency

1755-518: Is one of the most famous games in Game theory. The game is usually presented as follows: Two members of a criminal gang have been apprehended by the police. Both individuals now sit in solitary confinement. The prosecutors have the evidence required to put both prisoners away on lesser charges. However, they do not possess the evidence required to convict the prisoners on their principle charges. The prosecution therefore simultaneously offers both prisoners

1820-441: Is the maximin move (strategy), as it maximises the minimum possible payoff. Thus, the player can be assured a payoff of at least the maximin value, regardless of how the others are playing. The player doesn’t have the know the payoffs of the other players in order to choose the maximin move, therefore players can choose the maximin strategy in a simultaneous game regardless of what the other players choose. A pure Nash Equilibrium

1885-517: Is when no one can gain a higher payoff by deviating from their move, provided others stick with their original choices. Nash equilibria are self-enforcing contracts, in which negotiation happens prior to the game being played in which each player best sticks with their negotiated move. In a Nash Equilibrium, each player is best responded to the choices of the other player. The prisoner’s dilemma originated with Merrill Flood and Melvin Dresher and

1950-431: Is when the sum of payoffs equals zero for any outcome i.e. the losers pay for the winners gains. For a zero-sum 2-player game the payoff of player A doesn’t have to be displayed since it is the negative of the payoff of player B. An example of a simultaneous zero-sum 2-player game: Rock–paper–scissors is being played by two friends, A and B for $ 10. The first cell stands for a payoff of 0 for both players. The second cell

2015-458: The Battle Isle series of video games, players issue movement orders for all units in one phase, and attack orders in a later phase. In the board game Agricola (2007), turns are divided into three phases: "Upkeep", "Replenishing" and "Work." A fourth "Harvest" phase occurs every few turns. Some games that are generally real-time use turn-based play during specific sequences. For example,

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2080-520: The initiative statistic of each unit, no matter which side the unit belongs to. Games of this type are still technically sequential, as only one unit can perform an action at a time, and the duration of actions is not tied to the game clock. Examples include the video games The Temple of Elemental Evil (2003) and Final Fantasy Tactics (1997). Some games allow players to act outside of their normal turn by interrupting an opponent's turn and executing additional actions. The number and type of actions

2145-495: The role-playing video games Fallout (1997), Silent Storm (2003) and Baldur's Gate 3 (2023) are turn-based during the combat phase and real-time throughout the remainder of the game. This speeds up portions of the game where the careful timing of actions is not crucial to player success, such as exploration. Other video games, such as the Total War series, X-COM (1994) and Jagged Alliance 2 (1999), combine

2210-729: The V.A.T.S system in the real-time RPG Fallout 3 , where players could pause the game to target individual body parts. Final Fantasy XII (2006) expanded on active pause combat with its "gambits" system, which allows players to collect and apply preferences to the artificial intelligence routines of partner characters, who then perform certain actions in response to certain conditions. A similar "tactics" system later appeared in Dragon Age: Origins (2009) and Dragon Age II (2011). Knights of Xentar (1991) and Secret of Mana (1993) also allow an adjustable artificial intelligence to take control during combat. Some games use

2275-468: The best move a player can make is to follow their dominant strategy, if one exists. When analyzing a simultaneous game: Firstly, identify any dominant strategies for all players. If each player has a dominant strategy, then players will play that strategy however if there is more than one dominant strategy then any of them are possible. Secondly, if there aren’t any dominant strategies, identify all strategies dominated by other strategies. Then eliminate

2340-474: The challenge of deciding where to place troops in a shifting geopolitical battlefield. Other games in the Massive Assault line include: Turn-based Timekeeping is relevant to many types of games , including video games , tabletop role-playing games , board games , and sports . The passage of time must be handled in a way that players find fair and easy to understand. In many games, this

2405-475: The choices of other players. A simple example is an election in which not all voters will vote literally at the same time but each voter will vote not knowing what anyone else has chosen. Given that decision makers are rational, then so is individual rationality. An outcome is individually rational if it yields each player at least his security level. The security level for Player i is the amount max min Hi (s) that

2470-408: The constraints that Prisoners A and B are individually motivated, they will always choose betrayal. They do so by selecting the best option for themselves while considering each possible decisions of the other prisoner. In the battle of the sexes game, a wife and husband decide independently whether to go to a football game or the ballet. Each person likes to do something together with the other, but

2535-451: The course of a game. The game's factions include two main opposing forces: the heroic Free Nations Union, comparable to the UN, and the villainous Phantom League, a group of military organizations and corporations working together in secret. The units employed by each side are equivalent, without significant tactical differences. However, though both sides may select from a similar pool of units,

2600-402: The dominated strategies and the remaining are strategies players will play. Some people always expect the worst and believe that others want to bring them down when in fact others want to maximise their payoffs. Still, nonetheless, player A will concentrate on their smallest possible payoff, believing this is what player A will get, they will choose the option with the highest value. This option

2665-466: The enemy's turn. This is also implemented in some video games, such as Solasta: Crown of the Magister (2020). The Silent Storm video game series includes an "Interrupt" statistic for each character, to determine the likelihood of out-of-turn action. In the video game M.A.X. (1996), defensive units may be set to fire out of turn instead of on their own turn. In the board game Tide of Iron ,

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2730-409: The game to automatically pause when certain conditions are met, such as at the end of a round or upon the death of a non-player character . A variation of active pause, called "Smart Pause Mode" or SPM, is a feature of Apeiron's Brigade E5: New Jagged Union (2006) and 7.62: High Calibre (2007). The grand strategy games developed by Paradox Interactive exclusively use pausable real-time. It

2795-490: The game's rules permit a wide range of strategies and opponents need not select similar strategies. Players may select any of six geography types, varying from frozen, snowbound landscapes to tropical paradises. Each map features at least ten countries, with at least four allies for each of the two opponents. Countries are divided up into three categories: Undisclosed (secret) Ally, Disclosed Ally, and True Neutral. Since neither side discloses all their allies at once, players face

2860-414: The husband prefers football and the wife prefers ballet. The two Nash equilibria, and therefore the best responses for both husband and wife, are for them to both pick the same leisure activity e.g. (ballet, ballet) or (football, football). The table below shows the payoff for each option: Simultaneous games are designed to inform strategic choices in competitive and non cooperative environments. However,

2925-535: The mechanic was also present in earlier games such as in Knights of Xentar (1991), Darklands (1992), Tales of Phantasia (1995), Total Annihilation (1997) and Homeworld (1999). In Baldur's Gate , players may also let the artificial intelligence take control during combat and press the spacebar at any time to regain control of their characters. Further, in Baldur's Gate , players are able to configure

2990-510: The nodes, due to the party being unaware of the other party's decision (by definition of "simultaneous game"). Some variants of chess that belong to this class of games include synchronous chess and parity chess. In a simultaneous game, players only have one move and all players' moves are made simultaneously. The number of players in a game must be stipulated and all possible moves for each player must be listed. Each player may have different roles and options for moves. However, each player has

3055-727: The order of play using an initiative score based on players' attributes, positions within the game, or dice rolls. Dungeons & Dragons and Wizard101 are examples of this style. The term turn-based gaming is also used for play-by-mail games and browser-based gaming websites that allow long-term gameplay of board games such as Go and chess . Various adaptations of the real-time and turn-based systems have been implemented to address common or perceived shortcomings of these systems (though they often introduce new issues that did not exist before). These include: Timed turns are designed to prevent one player from using more time to complete turns than another. In chess , for instance,

3120-416: The other one will choose it is best to pick the option that is likely to give the you the greatest benefit for the lowest risk given the other player could choose anything i.e. if you pick your best option but the other player also picks their best option, someone will suffer. A dominant strategy provides a player with the highest possible payoff for any strategy of the other players. In simultaneous games,

3185-401: The other turns. In the video game King Arthur: The Role-Playing Wargame (2009), every fourth turn, the season turns to winter, the only time when buildings can be constructed. In the board game Napoleon (1974), every third player turn is a "night turn" when combat is not allowed. Other turn-based games feature several phases dedicated to different types of activities within each turn. In

3250-414: The other will choose to do. Thus, providing the potential for a player to receive no payoff should they be the only party to choose to hunt a Stag. Therefore, resulting in the following payoff matrix: The game is designed to illustrate a clear Pareto optimality where both players cooperate to hunt a Stag. However, due to the inherent risk of the game, such an outcome does not always come to fruition. It

3315-415: The other, by definition such representation does not correspond to the real life timing of the players’ decisions in a simultaneous game. The key to modeling simultaneous games in the extensive form is to get the information sets right. A dashed line between nodes in extensive form representation of a game represents information asymmetry and specifies that, during the game, a party cannot distinguish between

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3380-547: The outcome. Progress clocks are important in the heist film -inspired game Blades in the Dark and other games that adapt its Forged in the Dark system. Debates occur between fans of real-time and turn-based video games based on the merits and flaws of each timekeeping style. Arguments made in favor of turn-based systems include: Arguments made in favor of real-time systems include: Simultaneous game In sequential games, players observe what rivals have done in

3445-426: The past and there is a specific order of play. However, in simultaneous games, all players select strategies without observing the choices of their rivals and players choose at the exact same time. A simple example is rock-paper-scissors in which all players make their choice at the exact same time. However moving at exactly the same time isn’t always taken literally, instead players may move without being able to see

3510-402: The player can guarantee themselves unilaterally, that is, without considering the actions of other players. In a simultaneous game, players will make their moves simultaneously, determine the outcome of the game and receive their payoffs. The most common representation of a simultaneous game is normal form (matrix form). For a 2 player game; one player selects a row and the other player selects

3575-408: The player can pause the game to take aim with a weapon. In Vagrant Story , this allows players to target specific body parts while the game is paused. A similar mechanic was later used in the real-time role-playing game Last Rebellion (2010). Jagged Alliance 2 (1999) and Fallout (1997) allow players to target individual body parts during turn-based combat. The latter led to the creation of

3640-403: The player waited too long to issue a command, the game would issue a "pass" command automatically, thereby allowing enemies to take their turns while the player character did nothing. Time compression is a feature commonly found in real-time games such as flight simulators . It allows the player to speed up the game time by some (usually adjustable) factor. This permits the player to shorten

3705-514: The same amount of time has expired. In some real-time games, game actions are timed according to a common interval that is longer than the duration of play in the real world. For instance, non-player characters might only begin actions at the beginning or end of a round . Some video games such as the Baldur's Gate series use a rounds system based on tabletop role-playing games such as Dungeons & Dragons. The "Active Time Battle" (ATB) system

3770-460: The same options so if players interchange their moves, they also interchange their payoffs. By design, symmetric games are fair in which every player is given the same chances. Game theory should provide players with advice on how to find which move is best. These are known as “Best Response” strategies. Pure strategies are those in which players pick only one strategy from their best response. A Pure Strategy determines all your possible moves in

3835-634: The same or different rates from the passage of time in the real world. For example, in Terraria , one day-night cycle of 24 hours in the game is equal to 24 minutes in the real world. In a multiplayer real-time game, players perform actions simultaneously as opposed to in sequential units or turns. In competitive games, players must consider that their opponents are working against them in real time and may act at any moment. This introduces additional challenges. Many sports, such as soccer or basketball , are almost entirely simultaneous in nature, retaining

3900-500: The same time. One early example is the 1959 board game Diplomacy . Video game examples include Laser Squad Nemesis (2003), the Combat Mission series, Master of Orion series, Star Hammer: The Vanguard Prophecy (2015) and Battlestar Galactica Deadlock (2017). Clock-based games tie all unit actions directly to the game clock. Turns begin and end depending on the duration specified for each action, resulting in

3965-447: The subjective duration of long and relatively uneventful periods of gameplay. Many browser-based MMORPGs allocate a number of turns that can be played within a certain period of time, called a tick . A tick can be any measurement of real time. Players are allocated a certain number of turns per tick, which are refreshed at the beginning of each new tick. Tick-based games differ from other turn-based games in that ticks always occur after

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4030-474: The system. The ATB system was also used in Chrono Trigger (1995). In simultaneously executed games (also called "phase-based", "We-Go" or "Turn-based WeGo"), turns are separated into two distinct phases: decision and execution . In the decision phase, each player simultaneously plans and determines their units' actions. In the execution phase, all players' chosen actions occur automatically and at

4095-649: The table, the numbers in red represent the payoff to Player 1, the numbers in blue represent the payoff to Player 2. Hence, the pay off for a 2 player game in rock-paper-scissors will look like this: Another common representation of a simultaneous game is extensive form ( game tree ). Information sets are used to emphasize the imperfect information. Although it is not simple, it is easier to use game trees for games with more than 2 players. Even though simultaneous games are typically represented in normal form, they can be represented using extensive form too. While in extensive form one player’s decision must be draw before that of

4160-725: Was introduced by Hiroyuki Ito in Final Fantasy IV (1991). ATB combines turn-based combat with a continuous flow of actions and variable wait times. Enemies can attack or be attacked at any time. The ATB system was further developed in Final Fantasy V (1992), which introducing a time gauge showing which character's turn is next. The ATB system has since been used in VI (1994), VII (1997), VIII (1999), IX (2000), and X-2 (2003). Both Final Fantasy XII (2006) and XIII (2009) used heavily modified versions of

4225-581: Was the originally intended mode of the Civilization series before the developers decided to switch to turn-based. It has been present in the SimCity construction and management simulation series since SimCity (1989) and is also used in the Transport Tycoon and RollerCoaster Tycoon series. In the single-character console RPGs Parasite Eve (1998) and Vagrant Story (2000),

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